Show that if the prime power factorization of n-1 is p1^a1...pt^at and that there exists integers xj , for j = 1,2,3,...,t such that for each j:
xj^[(n-1)/pj] is not congruent to 1 (mod n)
xj^(n-1) is congruent to 1 (mod n)
then n is a prime.
Any ideas on how to prove the above? Thanks