Prove regarding number of distinct polynomial roots

Question

Prove that for any g(x) in a $\mathbb{Z}/p\mathbb{Z}[x]$ field, the degree of $\gcd{(x^p-x,g(x))}$ is equal to the number of distinct roots of g(x)
First of all, I am assuming that the "number of distinct roots" refer to the number of distinct roots of g(x) in the mod p field
Secondly, where should I start to go about proving this?