{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-06T14:01:22.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-04-06T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":57447,"title":"Compute a nested cube root","description":"Consider the quantity . Write a function to compute  without using loops or recursion. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 68.075px 8px; transform-origin: 68.075px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eConsider the quantity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"y = (a+(a+(a+(a+...)^{1/3})^{1/3})^{1/3})^{1/3}\" style=\"width: 249px; height: 19.5px;\" width=\"249\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 90.875px 8px; transform-origin: 90.875px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Write a function to compute \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ey\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 71.575px 8px; transform-origin: 71.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e without using loops or recursion. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = nestedCubeRoot(a)\r\n  y = nthroot(a+nthroot(a+nthroot(a+nthroot(a,3),3),3),3);\r\nend","test_suite":"%%\r\na = 6;\r\nassert(abs(nestedCubeRoot(a)-2)\u003c1e-14)\r\n\r\n%%\r\na = 24;\r\nassert(abs(nestedCubeRoot(a)-3)\u003c1e-14)\r\n\r\n%%\r\na = 120;\r\nassert(abs(nestedCubeRoot(a)-5)\u003c1e-14)\r\n\r\n%%\r\na = 336;\r\nassert(abs(nestedCubeRoot(a)-7)\u003c1e-14)\r\n\r\n%%\r\na = 1320;\r\nassert(abs(nestedCubeRoot(a)-11)\u003c1e-14)\r\n\r\n%%\r\na = 15/8;\r\nassert(abs(nestedCubeRoot(a)-3/2)\u003c1e-14)\r\n\r\n%%\r\na = 2040/2197;\r\nassert(abs(nestedCubeRoot(a)-17/13)\u003c1e-14)\r\n\r\n%%\r\na = 9048/12167;\r\nassert(abs(nestedCubeRoot(a)-29/23)\u003c1e-14)\r\n\r\n%%\r\na = 29520/29791;\r\nassert(abs(nestedCubeRoot(a)-41/31)\u003c1e-14)\r\n\r\n%%\r\na = 117384/226981;\r\nassert(abs(nestedCubeRoot(a)-73/61)\u003c1e-14)\r\n\r\n%%\r\na = 2259912/3869893;\r\nassert(abs(nestedCubeRoot(a)-191/157)\u003c1e-14)\r\n\r\n%%\r\nfiletext = fileread('nestedCubeRoot.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || contains(filetext, 'switch') || contains(filetext,'for') || contains(filetext,'while') || length(strfind(filetext,'nestedCubeRoot')) \u003e 1;\r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-12-21T13:18:24.000Z","deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-12-21T13:13:13.000Z","updated_at":"2026-03-04T12:08:30.000Z","published_at":"2022-12-21T13:18:25.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider the quantity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y = (a+(a+(a+(a+...)^{1/3})^{1/3})^{1/3})^{1/3}\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey = (a+(a+(a+(a+\\\\ldots)^{1/3})^{1/3})^{1/3})^{1/3}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Write a function to compute \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e without using loops or recursion. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":58946,"title":"Count block fountains","description":"A block fountain consists of rows of circles in which each row is a continuous block of circles (i.e., adjacent circles are tangent) and each circle in a row above the first touches exactly two circles on the previous row. \r\nWrite a function to compute the number of block fountains with  circles on the first row. For example, there are five block fountains with three circles on the first row. \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 429.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 214.85px; transform-origin: 407px 214.85px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 364.85px 8px; transform-origin: 364.85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA block fountain consists of rows of circles in which each row is a continuous block of circles (i.e., adjacent circles are tangent) and each circle in a row above the first touches exactly two circles on the previous row. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 195.125px 8px; transform-origin: 195.125px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the number of block fountains with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 176.958px 8px; transform-origin: 176.958px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e circles on the first row. For example, there are five block fountains with three circles on the first row. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 327.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 163.85px; text-align: left; transform-origin: 384px 163.85px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"543\" height=\"322\" style=\"vertical-align: baseline;width: 543px;height: 322px\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = blockFountain(n)\r\n  y = factorial(n);\r\nend","test_suite":"%%\r\nassert(isequal(blockFountain(3),5))\r\n\r\n%%\r\nassert(isequal(blockFountain(5),34))\r\n\r\n%%\r\nassert(isequal(blockFountain(8),610))\r\n\r\n%%\r\nassert(isequal(blockFountain(14),196418))\r\n\r\n%%\r\nassert(isequal(blockFountain(14),196418))\r\n\r\n%%\r\nassert(isequal(blockFountain(23),1134903170))\r\n\r\n%%\r\nassert(isequal(blockFountain(28),139583862445))\r\n\r\n%%\r\nassert(isequal(blockFountain(33),17167680177565))\r\n\r\n%%\r\nassert(isequal(blockFountain(35),117669030460994))\r\n\r\n%%\r\nfiletext = fileread('blockFountain.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'switch'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":4,"created_by":46909,"edited_by":46909,"edited_at":"2023-09-03T17:54:36.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":"2023-09-03T17:54:19.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-09-02T14:47:44.000Z","updated_at":"2026-01-26T19:21:38.000Z","published_at":"2023-09-02T14:47:49.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA block fountain consists of rows of circles in which each row is a continuous block of circles (i.e., adjacent circles are tangent) and each circle in a row above the first touches exactly two circles on the previous row. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the number of block fountains with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e circles on the first row. For example, there are five block fountains with three circles on the first row. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"322\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"543\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57477,"title":"Solve an equation involving primes and fractions","description":"Write a function to find pairs of primes  and  satisfying the equation\r\n\r\nwhere  is an integer. The function should take a number  as input and produce the triples , , and  such that . If there are no solutions, the function should return three empty vectors.\r\nThis problem is adapted from one in the 2012 European Girls’ Math Olympiad. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 146px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 343px 73px; transform-origin: 343px 73px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 10.5px; text-align: left; transform-origin: 320px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWrite a function to find pairs of primes \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ep\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eq\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e satisfying the equation\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 35px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 17.5px; text-align: left; transform-origin: 320px 17.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"136\" height=\"35\" alt=\"p/(p+1) + (q+1)/q = 2n/(n+2)\" style=\"width: 136px; height: 35px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 21px; text-align: left; transform-origin: 320px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is an integer. The function should take a number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e as input and produce the triples \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ep\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eq\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e such that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"38\" height=\"18\" alt=\"p \u003c= x\" style=\"width: 38px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. If there are no solutions, the function should return three empty vectors.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 10.5px; text-align: left; transform-origin: 320px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis problem is adapted from one in the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.egmo2012.org.uk/\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003e2012 European Girls’ Math Olympiad\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [p,q,n] = EGMO2012no5(x)\r\n  p = primes(x); q = primes(x); n = p./(p+1) + (q+1)./q; \r\nend","test_suite":"%%\r\nx = 1;\r\n[p,q,n] = EGMO2012no5(x);\r\nassert(isempty(p) \u0026\u0026 isempty(q) \u0026\u0026 isempty(n))\r\n\r\n%%\r\nx = 2;\r\n[p,q,n] = EGMO2012no5(x);\r\nassert(all(p==2) \u0026\u0026 isequal(q,[5 7]) \u0026\u0026 isequal(n,[28 19]))\r\n\r\n%%\r\nx = 20;\r\n[p,q,n] = EGMO2012no5(x);\r\ns_correct = [35 28 86 178 646 1402];\r\nassert(isequal(p+q+n,s_correct))\r\n\r\n%%\r\nx = 200;\r\n[p,q,n] = EGMO2012no5(x);\r\ns_correct = [35 28 86 178 646 1402 3778 7306 14758 21166 42226 47302 77002 90898 130678 148606 158002];\r\nassert(isequal(p+q+n,s_correct))\r\n\r\n%%\r\nx = 2000;\r\n[p,q,n] = EGMO2012no5(x);\r\nlen_correct = 63;\r\nsum_correct = 265170305;\r\nassert(isequal(length(p),len_correct) \u0026\u0026 isequal(sum(p+q+n),sum_correct))\r\n\r\n%%\r\nx = 20000;\r\n[p,q,n] = EGMO2012no5(x);\r\nlen_correct = 344;\r\nsum_correct = 150118037395;\r\nassert(isequal(length(p),len_correct) \u0026\u0026 isequal(sum(p+q+n),sum_correct))\r\nassert(all(isprime(p)) \u0026\u0026 all(isprime(q)))\r\n\r\n%%\r\nx = 2000000;\r\n[p,q,n] = EGMO2012no5(x);\r\nlen_correct = 14873;\r\nsum_correct = 27402595128;\r\nassert(isequal(length(p),len_correct) \u0026\u0026 isequal(sum(p+q),sum_correct))\r\nassert(all(isprime(p)) \u0026\u0026 all(isprime(q)))\r\n\r\n%%\r\nx = 2e8;\r\n[p,q,n] = EGMO2012no5(x);\r\nlen_correct = 813373;\r\nsum_correct = 152663390088360;\r\nassert(isequal(length(p),len_correct) \u0026\u0026 isequal(sum(p+q),sum_correct))\r\n\r\n%%\r\nfiletext = fileread('EGMO2012no5.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-12-30T13:15:49.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-12-30T05:04:32.000Z","updated_at":"2025-12-14T08:06:30.000Z","published_at":"2022-12-30T05:05:56.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to find pairs of primes \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eq\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e satisfying the equation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p/(p+1) + (q+1)/q = 2n/(n+2)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{p}{p+1} + \\\\frac{q+1}{q} = \\\\frac{2n}{n+2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is an integer. The function should take a number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e as input and produce the triples \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eq\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e such that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p \u0026lt;= x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep \\\\le x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. If there are no solutions, the function should return three empty vectors.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem is adapted from one in the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.egmo2012.org.uk/\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2012 European Girls’ Math Olympiad\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":57447,"title":"Compute a nested cube root","description":"Consider the quantity . Write a function to compute  without using loops or recursion. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 68.075px 8px; transform-origin: 68.075px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eConsider the quantity \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"y = (a+(a+(a+(a+...)^{1/3})^{1/3})^{1/3})^{1/3}\" style=\"width: 249px; height: 19.5px;\" width=\"249\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 90.875px 8px; transform-origin: 90.875px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Write a function to compute \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ey\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 71.575px 8px; transform-origin: 71.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e without using loops or recursion. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = nestedCubeRoot(a)\r\n  y = nthroot(a+nthroot(a+nthroot(a+nthroot(a,3),3),3),3);\r\nend","test_suite":"%%\r\na = 6;\r\nassert(abs(nestedCubeRoot(a)-2)\u003c1e-14)\r\n\r\n%%\r\na = 24;\r\nassert(abs(nestedCubeRoot(a)-3)\u003c1e-14)\r\n\r\n%%\r\na = 120;\r\nassert(abs(nestedCubeRoot(a)-5)\u003c1e-14)\r\n\r\n%%\r\na = 336;\r\nassert(abs(nestedCubeRoot(a)-7)\u003c1e-14)\r\n\r\n%%\r\na = 1320;\r\nassert(abs(nestedCubeRoot(a)-11)\u003c1e-14)\r\n\r\n%%\r\na = 15/8;\r\nassert(abs(nestedCubeRoot(a)-3/2)\u003c1e-14)\r\n\r\n%%\r\na = 2040/2197;\r\nassert(abs(nestedCubeRoot(a)-17/13)\u003c1e-14)\r\n\r\n%%\r\na = 9048/12167;\r\nassert(abs(nestedCubeRoot(a)-29/23)\u003c1e-14)\r\n\r\n%%\r\na = 29520/29791;\r\nassert(abs(nestedCubeRoot(a)-41/31)\u003c1e-14)\r\n\r\n%%\r\na = 117384/226981;\r\nassert(abs(nestedCubeRoot(a)-73/61)\u003c1e-14)\r\n\r\n%%\r\na = 2259912/3869893;\r\nassert(abs(nestedCubeRoot(a)-191/157)\u003c1e-14)\r\n\r\n%%\r\nfiletext = fileread('nestedCubeRoot.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || contains(filetext, 'switch') || contains(filetext,'for') || contains(filetext,'while') || length(strfind(filetext,'nestedCubeRoot')) \u003e 1;\r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-12-21T13:18:24.000Z","deleted_by":null,"deleted_at":null,"solvers_count":17,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-12-21T13:13:13.000Z","updated_at":"2026-03-04T12:08:30.000Z","published_at":"2022-12-21T13:18:25.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider the quantity \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y = (a+(a+(a+(a+...)^{1/3})^{1/3})^{1/3})^{1/3}\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey = (a+(a+(a+(a+\\\\ldots)^{1/3})^{1/3})^{1/3})^{1/3}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Write a function to compute \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"y\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e without using loops or recursion. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":58946,"title":"Count block fountains","description":"A block fountain consists of rows of circles in which each row is a continuous block of circles (i.e., adjacent circles are tangent) and each circle in a row above the first touches exactly two circles on the previous row. \r\nWrite a function to compute the number of block fountains with  circles on the first row. For example, there are five block fountains with three circles on the first row. \r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 429.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 214.85px; transform-origin: 407px 214.85px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 364.85px 8px; transform-origin: 364.85px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA block fountain consists of rows of circles in which each row is a continuous block of circles (i.e., adjacent circles are tangent) and each circle in a row above the first touches exactly two circles on the previous row. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 195.125px 8px; transform-origin: 195.125px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the number of block fountains with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 176.958px 8px; transform-origin: 176.958px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e circles on the first row. For example, there are five block fountains with three circles on the first row. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 327.7px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 163.85px; text-align: left; transform-origin: 384px 163.85px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"543\" height=\"322\" style=\"vertical-align: baseline;width: 543px;height: 322px\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = blockFountain(n)\r\n  y = factorial(n);\r\nend","test_suite":"%%\r\nassert(isequal(blockFountain(3),5))\r\n\r\n%%\r\nassert(isequal(blockFountain(5),34))\r\n\r\n%%\r\nassert(isequal(blockFountain(8),610))\r\n\r\n%%\r\nassert(isequal(blockFountain(14),196418))\r\n\r\n%%\r\nassert(isequal(blockFountain(14),196418))\r\n\r\n%%\r\nassert(isequal(blockFountain(23),1134903170))\r\n\r\n%%\r\nassert(isequal(blockFountain(28),139583862445))\r\n\r\n%%\r\nassert(isequal(blockFountain(33),17167680177565))\r\n\r\n%%\r\nassert(isequal(blockFountain(35),117669030460994))\r\n\r\n%%\r\nfiletext = fileread('blockFountain.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'switch'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":4,"created_by":46909,"edited_by":46909,"edited_at":"2023-09-03T17:54:36.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":"2023-09-03T17:54:19.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-09-02T14:47:44.000Z","updated_at":"2026-01-26T19:21:38.000Z","published_at":"2023-09-02T14:47:49.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA block fountain consists of rows of circles in which each row is a continuous block of circles (i.e., adjacent circles are tangent) and each circle in a row above the first touches exactly two circles on the previous row. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the number of block fountains with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e circles on the first row. For example, there are five block fountains with three circles on the first row. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"322\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"543\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57477,"title":"Solve an equation involving primes and fractions","description":"Write a function to find pairs of primes  and  satisfying the equation\r\n\r\nwhere  is an integer. The function should take a number  as input and produce the triples , , and  such that . If there are no solutions, the function should return three empty vectors.\r\nThis problem is adapted from one in the 2012 European Girls’ Math Olympiad. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 146px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 343px 73px; transform-origin: 343px 73px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 10.5px; text-align: left; transform-origin: 320px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWrite a function to find pairs of primes \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ep\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eq\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e satisfying the equation\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 35px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 17.5px; text-align: left; transform-origin: 320px 17.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"136\" height=\"35\" alt=\"p/(p+1) + (q+1)/q = 2n/(n+2)\" style=\"width: 136px; height: 35px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 21px; text-align: left; transform-origin: 320px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is an integer. The function should take a number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e as input and produce the triples \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ep\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eq\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e such that \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"38\" height=\"18\" alt=\"p \u003c= x\" style=\"width: 38px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. If there are no solutions, the function should return three empty vectors.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 320px 10.5px; text-align: left; transform-origin: 320px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis problem is adapted from one in the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.egmo2012.org.uk/\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003e2012 European Girls’ Math Olympiad\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [p,q,n] = EGMO2012no5(x)\r\n  p = primes(x); q = primes(x); n = p./(p+1) + (q+1)./q; \r\nend","test_suite":"%%\r\nx = 1;\r\n[p,q,n] = EGMO2012no5(x);\r\nassert(isempty(p) \u0026\u0026 isempty(q) \u0026\u0026 isempty(n))\r\n\r\n%%\r\nx = 2;\r\n[p,q,n] = EGMO2012no5(x);\r\nassert(all(p==2) \u0026\u0026 isequal(q,[5 7]) \u0026\u0026 isequal(n,[28 19]))\r\n\r\n%%\r\nx = 20;\r\n[p,q,n] = EGMO2012no5(x);\r\ns_correct = [35 28 86 178 646 1402];\r\nassert(isequal(p+q+n,s_correct))\r\n\r\n%%\r\nx = 200;\r\n[p,q,n] = EGMO2012no5(x);\r\ns_correct = [35 28 86 178 646 1402 3778 7306 14758 21166 42226 47302 77002 90898 130678 148606 158002];\r\nassert(isequal(p+q+n,s_correct))\r\n\r\n%%\r\nx = 2000;\r\n[p,q,n] = EGMO2012no5(x);\r\nlen_correct = 63;\r\nsum_correct = 265170305;\r\nassert(isequal(length(p),len_correct) \u0026\u0026 isequal(sum(p+q+n),sum_correct))\r\n\r\n%%\r\nx = 20000;\r\n[p,q,n] = EGMO2012no5(x);\r\nlen_correct = 344;\r\nsum_correct = 150118037395;\r\nassert(isequal(length(p),len_correct) \u0026\u0026 isequal(sum(p+q+n),sum_correct))\r\nassert(all(isprime(p)) \u0026\u0026 all(isprime(q)))\r\n\r\n%%\r\nx = 2000000;\r\n[p,q,n] = EGMO2012no5(x);\r\nlen_correct = 14873;\r\nsum_correct = 27402595128;\r\nassert(isequal(length(p),len_correct) \u0026\u0026 isequal(sum(p+q),sum_correct))\r\nassert(all(isprime(p)) \u0026\u0026 all(isprime(q)))\r\n\r\n%%\r\nx = 2e8;\r\n[p,q,n] = EGMO2012no5(x);\r\nlen_correct = 813373;\r\nsum_correct = 152663390088360;\r\nassert(isequal(length(p),len_correct) \u0026\u0026 isequal(sum(p+q),sum_correct))\r\n\r\n%%\r\nfiletext = fileread('EGMO2012no5.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp'); \r\nassert(~illegal)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":46909,"edited_by":46909,"edited_at":"2022-12-30T13:15:49.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-12-30T05:04:32.000Z","updated_at":"2025-12-14T08:06:30.000Z","published_at":"2022-12-30T05:05:56.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to find pairs of primes \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eq\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e satisfying the equation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p/(p+1) + (q+1)/q = 2n/(n+2)\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{p}{p+1} + \\\\frac{q+1}{q} = \\\\frac{2n}{n+2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is an integer. The function should take a number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e as input and produce the triples \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"q\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eq\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"n\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e such that \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"p \u0026lt;= x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ep \\\\le x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. 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