# Solution May 30, 2009

*Sketch of Proof*.

It's easy to see that is divisible by *p*^{n − 1}. Then,

Modulo *p*, it's clear that the right hand side is divisible by *p*.

For the variation when *p* is an odd prime, it suffices to check that *p*^{n + 1} divides .

. But by wilson's theorem + the fact that every element has unique inverse.