State Euler's criterion.

Let $p$ be an odd prime. Show that every primitive root modulo $p$ is a quadratic non-residue modulo $p$.

Let $p$ be a Fermat prime, that is, a prime of the form $2^{2^{k}}+1$ for some $k \geqslant 1$. By evaluating $\phi(p-1)$, or otherwise, show that every quadratic non-residue modulo $p$ is a primitive root modulo $p$. Deduce that 3 is a primitive root modulo $p$ for every Fermat prime $p$.