Quote:
Originally Posted by RMLabrador
Theorem 1 also works for composites.
Yes.There is a lot of exeption. For some values u. Carmichael numbers do it even for many of u, but there is not a problem.
Not exist such exeption that have BOTH type of resudials for some different u, if so, this numbers is prime.

Code:
[n,u,w]=[1247, 601, 638];Mod([1,1;1,u],n)^(n)==[u,1;1,1]&&Mod([1,1;1,w],n)^(n)==[1,1;1,w]
1
Quote:
Quote:
Theorem 2 is illdefined. What are a(u) and c(u). Can you give a numerical example how this works?

a(u), c(u), b(u)  polynomial of u, result of analytical powering of matrix.
p=5
u^4+u^3+4u^2+5u+5 (1)
5u+2=7u, substitute
u^429u^3+319u^21580u+2980 (2)
(1)(2)=5(2u7)(3u^221u+85)
(2u7)(3u^221u+85) = g(u)
5=p
That true ONLY if p is prime.

I will have to think more about what you are writing.