my error in the write n!+1 = 0 mod n

n=1:500;
n_true = [];
for i=1:length(n)
    x = 2:n(i);
 
   
       nq=factorial(n(i)))+1;
   x3 = mod(0,n(i));
    if ~any(x3 == nq) 
        n_true(end+1) = n(i);
    
    end
end


i want find all n values by n!+1 = 0 mod n

[the cyclist]

I did not look for errors in your code, but be aware that factorial(n) will return Inf, for values larger than 169:

factorial(168:172)

so your code will likely not do what you expect. Even for smaller values of n, it might not be accurate.

[Steven Lord]

By the definition of the factorial function, factorial(n) is equivalent to 0 mod n as it is n*factorial(n-1). [The base case where n = 0 is handled by the convention, listed on the mod documentation page, that mod(x, 0) is x.] So you're looking for values of n for which 1 is also equivalent to 0 mod n. That would mean 1 is an integer multiple of n. For how many values of n is this true?

[Dipankar]

it was tried to found out the solution of Brocards problem

Answer 1

[Jan]

nq=factorial(n(i)))+1;
%                 ^

Here are more closing then opening parentheses.

Whenever you mention an error in the forum, attach a copy of the complete message.

This is strange also:

x3 = mod(0,n(i))

This checks, if 0 is divisable by n(i). Even the equation n!+1 = 0 mod n looks confusing.

[the cyclist]

I think he is trying to find n where

mod(factorial(n)+1,n) == 0

Note that for small n, this can be done without any loop:

n = 1:10;
find(mod(factorial(n)+1,n) == 0)

ans = 1

One might need to resort to the Symbolic Toolbox for larger n. I actually tried to do this, and did not find any more values than n==1, but I am not confident enough in my use of that toolbox to be sure that I did not make a mistake, so I did not post an answer. But this is the code I used:

syms n

tf = mod(factorial(n)+1,n)==0;

n = 1:500;

find(eval(subs(tf)))

ans = 1

I searched values of n up to 100,000.

[Walter Roberson]

n factorial is divisible by n for positive n. Adding 1 is going to give something not divisible by n except for the case where 1 is divisible by n

[the cyclist]

Of course. Now I feel dumb. Well, dumber than usual. :-)

[Mohammed AL Rashedi]

Dear the cyclist exactly, "I think he is trying to find n where" .Thank you Walter Roberson .

Thank you guys. I love you