# Prime number Proof

• Nov 23rd 2009, 08:29 AM
MichaelG
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
• Nov 23rd 2009, 08:34 AM
qmech
wilson's theorem
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).

Note that $a^p \equiv a \mod{p} \; \forall a$ though.