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Old 2020-09-11, 15:40   #3
RMLabrador
 
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"Roman V. Makarchuk"
Aug 2020
Ukraine

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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.


Theorem 2 is ill-defined. What are a(u) and c(u). Can you give a numerical example how this works?[/QUOTE]

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.

Last fiddled with by RMLabrador on 2020-09-11 at 15:44
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