Prime number Proof

If p is prime, prove that for any integer a, p divides a^p + (p-1)!a and p divides (p-1)!a^p + a

For a prime p Wilson's theorem says that (p-1)! = -1 mod p.

Also, Fermat's little theorem says that for a s.t. (a,p) = 1 (no common factor), a^(p-1) = 1 (p), which implies that a^p = a (p).

Try these in your problem.

Note that though.