Proof

p|n^3-1=(n-1)(n^2+n+1), since p is prime and n < p, we have p | n^2+n+1. On the other hand, n | p - 1.

So there are integers k and x such that p-1=kn and n^2+n+1=p x= knx + x. Take (mod n), x=1

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• 好，这个简洁 -魁北克人- ♂ (9 bytes) () 10/18/2014 postreply 07:24:34