Let $\displaystyle p$ be an odd prime number. Show that there are infinitely many prime numbers that are quadratic residues modulo $\displaystyle p$. Show that there are infinitely many prime numbers that are quadratic nonresidues modulo $\displaystyle p$.

I actually really don't know how to go about proving this. I thought Euler's Criterion or the laws of quadratic reciprocity might help but I have no idea how to apply them for this question.