Suppose $p$ is an odd prime. Show that $1^{p-1} +2^{p-1}+ \ldots +(p-1)^{p-1}\equiv -1\pmod p$ Suppose $p$ is an odd prime.  Show that $1^{p-1} +2^{p-1}+ \ldots +(p-1)^{p-1}\equiv -1\pmod p$. 
I think I need to use Wilson's Theorem on this but I'm not sure how. 
I believe I am suppose to factor it somehow too but also I'm lost at this point.

Use Fermat's Little Theorem on each term, and then count the terms.
