How do i prove the following theorem?
Supose $p$ is a prime number, $r,\ s$ are positive integers and $x$ is an arbitary integer. Then we have $x^r \equiv x^s\ (mod\ p)$ whenever $r \equiv s \ (mod \ p-1)$.
I'm thinking of using order of powers formula:
$m^r = 1\ (mod\ n)$
and FTL:
$a^{p-1} = 1 \ (mod \ p)$
but im not sure what to do really.