Let $p, q$ be distinct odd primes, and with $p \equiv 1 \mod \ 4$. If $p \equiv x^2 \mod\ q$ for some integer $x$ (i.e. $p$ is a quadratic residue mod q), then show $p \equiv b^2 \mod\ 4q $ for some odd integer $b$.
Cox's book "Primes of the form x^2 + ny^2" on p.14 says (something slightly more general than the above) is straightforward, but I'm not seeing how.