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Search for seesaw primes
Cody Problem 60958 introduced seesaw numbers. A number is a seesaw number if the next smaller numbers can be placed on a seesa...

3 months ago

Solved

Find the Prime Factors and Divisors of a Number
Given a positive integer n, find its prime factors as well as all of its divisors. Example: n=12 has prime factors [2,2,3] and ...

3 months ago

Solved

List numbers that cannot be expressed as the sum of two primes
The Goldbach conjecture claims that even numbers greater than 2 can be expressed as the sum of two prime numbers. What about the...

3 months ago

Solved

List even numbers whose Goldbach partition does not use the largest prime
The strong Goldbach conjecture says that every even number greater than 2 can be expressed as a sum of two prime numbers—that is...

3 months ago

Solved

List balanced primes
A balanced prime of order is one that equals the average of the primes before it and the primes after it. For example, 79 is ...

3 months ago

Solved

Mesh the cube
Problem statement : mesh the cube with quadranglar / squared faces An cube / regular hexahedron is a regular polyhedron with ...

3 months ago

Solved

Mesh the convex hull of a random 3D point cloud
Problem statement The convex hull of a 3D point set is actually a first -though rough- triangulation of it. Use Matlab funct...

3 months ago

Solved

Build triangulation from -sorted- edge list
Problem statement An edge list is simply a N x 2 matrix of positive integers, in which N is the number of edges and each intege...

3 months ago

Solved

Mesh the icosahedron
Problem statement An icosahedron is a regular polyhedron with 12 vertices and 20 triangular faces. It is also one of the five...

3 months ago

Solved

Mesh the dodecahedron
Problem statement An dodecahedron is a regular polyhedron with 20 vertices and 12 pentagonal faces. It is also one of the fiv...

3 months ago

Solved

Check Euler's characteristic on regular polyhedra
Problem statement Given the number of vertices and the number of faces of a given regular polyhedron, compute the number of its...

3 months ago

Solved

Mesh the square with triangles
Problem statement An square is a regular polygon with 4 vertices and 4 edges. Here below is an example of the vertex set V, c...

3 months ago

Solved

Mesh the pentagon (with the minimum number of triangles)
Problem statement An pentagon is a regular polygon with 5 vertices and 5 edges. Here below is an example of the vertex set V,...

3 months ago

Solved

Mesh the tetrahedron
Problem statement An tetrahedron is a regular polyhedron with 4 vertices and 4 triangular faces. It is also one of the five w...

3 months ago

Solved

Mesh the octahedron
Problem statement An octahedron is a regular polyhedron with 6 vertices and 8 triangular faces. It is also one of the five we...

3 months ago

Solved

Linear primes p' = mp + n
Problem statement List the prime numbers of the form p' = mp + n for a given (m,n) couple and such that p' < k, k positive in...

3 months ago

Solved

Check Bertrand-Chebyshev's theorem about prime numbers
Historical context Bertrand's postulate, also later known as Chebyshev's theorem, is a very important theorem in number theory ...

3 months ago

Solved

List the twin prime couples
Problem statement The twin prime couples (p,p') are the ones such that p' = p + 2. For a given integer n > 1, list the twin p...

3 months ago

Solved

List the complementary / symetric prime couples
Problem statement For a given positive integer n, provide the prime couples (p,p') such that p + p' = 10^n. NB : a number li...

3 months ago

Solved

Check Legendre's conjecture
Context and problem statement Legendre's conjecture states for a given positive integer n, there always exists at least one pri...

3 months ago

Solved

Evaluate Deterministic Finite Automata on String
Given a Deterministic Finite Automata (DFA) and a string, determine whether or not the DFA will accept when ran on the string. A...

3 months ago

Solved

Check p = 6n +/- 1, the generic formula for odd prime numbers greater than 3
Problem statement For all odd prime number p greater than 3, there exists a positive integer n, such that p = 6n +/- 1 : ...

3 months ago

Solved

Check p = 4n +/- 1, the generic formula for odd prime numbers
Problem statement For all odd prime number p, there exists a positive integer n, such that p = 4n +/- 1 : Check this f...

3 months ago

Solved

Monkey and the Peaches
A monkey picked a certain number of peaches on the first day. Each day, the monkey eats half of the remaining peaches plus one ...

3 months ago

Solved

Determine if LTI system with feedback control is stable
Linear timeiinvariant systems can be represented by the differential equation , where is an matrix, is an vector representing...

3 months ago

Solved

List primes which are the sum of two consecutive lower primes plus minus one
Problem statement Some prime numbers can be written as the sum of two consecutive lower primes plus / minus one : Like t...

3 months ago

Solved

List the near-square primes, p = n² + 1 (Landau's 4th problem)
Historical context At the 1912 International Congress of Mathematicians, Edmund Landau listed four basic problems about prime...

3 months ago

Solved

Determine whether a number is a seesaw number
Cody Problem 60957 dealt with balanced primes. In that case, balance was measured in terms of the average of primes around a giv...

3 months ago

Solved

List mean-of-2 primes
The prime number 53 is the average of the first prime before it (47) and the first prime after it (59), and the prime number 11 ...

3 months ago

Solved

Chek the Delta = 6k gap conjecture about arithmetic progressions in the prime number set
Context In the prime numbers set there are some arithmetic progressions (sequences of three or more consecutive prime number...

4 months ago