Let p be an odd prime. Prove that every primitive root of p is a quadratic nonresidue. Prove that every quadratic nonresidue is a primitive root if and only if $\displaystyle p$ is of the form $\displaystyle 2^{2^n} + 1$ where $\displaystyle n$ is a non-negative integer, that is, if and only if $\displaystyle p=3 \mbox{ or } p$ is a Fermat number.

I have no clue what to do.