Let is a positive integer. Prove that is a prime if and only if . I have no clue on how to start.
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since . Therefore for a fixed , there exists a unique such that . Hence if we partition into such that , we get . By Wilson's Theorem we have is prime. I'm not exactly sure this is right so if someone wants to confirm this, that would be great.
Originally Posted by chiph588@ Therefore for a fixed , there exists a unique such that . your idea is good but the above conclusion is unfortunately not true at least when is not prime (choose to be any divisor of ). you probably meant has a unique solution modulo which is correct but not very useful here.
Well one way is easy. If is prime then by Euler's Criterion. .
Thank you so much. By the way, how did you get from ?
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