So I have the following problem: Prove that if $\displaystyle x$ is prime and $\displaystyle n$ is not an integer multiple of $\displaystyle x$, then $\displaystyle n^{x-1} \equiv 1 \mod{x}$. I could really use some help getting this problem started and would appreciate a nudge in the correct direction. Thanks for any help.
So I have the following problem: Prove that if $\displaystyle x$ is prime and $\displaystyle n$ is not an integer multiple of $\displaystyle x$, then $\displaystyle n^{x-1} \equiv 1 \mod{x}$. I could really use some help getting this problem started and would appreciate a nudge in the correct direction. Thanks for any help.