If

n > 1 is an integer and for each prime factor q of n-1 there is an an integer a such that and a^(n-1)=1 (mod n),

but a^((n-1)/q) != 1 (mod n), then n is prime.

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- October 8th 2009, 05:12 PMkobulingamTough prime testing question
If

n > 1 is an integer and for each prime factor q of n-1 there is an an integer a such that and a^(n-1)=1 (mod n),

but a^((n-1)/q) != 1 (mod n), then n is prime.

- October 9th 2009, 02:41 AMaidan
I don't see a question.

That is a statement of the Lucas primality test.

An explanation for the correctness of that is here: Lucas primality test - Wikipedia, the free encyclopedia