Here's a little number theory problem I'm wrestling with.
Let $p$ and $q$ be odd prime numbers with $p=q+4a$ for some $a \in \mathbb{Z}$. Prove that $$\left( \frac{a}{p} \right) = \left( \frac{a}{q} \right),$$
where $\left( \frac{a}{p} \right)$ is the Legendre symbol. I have been trying to use the law of quadratic reciprocity but to no avail. Can you help?