Legendre symbols and primitive roots modulo $p$

Question

Suppose that $\omega$ is a primitive root modulo $p$. What is $(\frac{\omega}{p})$?

$p$ is prime.

Answer 1

Hint: If $x$ is a (nonzero) quadratic residue $\bmod p$, then

$$x^{\frac{p-1}{2}}\equiv 1\bmod p.$$