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Old 2020-09-11, 16:15   #4
paulunderwood
 
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Sep 2002
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Quote:
Originally Posted by RMLabrador View Post
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 ill-defined. 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)
5-u+2=7-u, substitute
u^4-29u^3+319u^2-1580u+2980 (2)

(1)-(2)=5(2u-7)(3u^2-21u+85)
(2u-7)(3u^2-21u+85) = g(u)

5=p
That true ONLY if p is prime.
I will have to think more about what you are writing.

Last fiddled with by paulunderwood on 2020-09-11 at 16:15
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