I'm working on the following problems concerning quadratic reciprocity.
a) Use the Law of Quadratic Reciprocity and the Chinese Remainder Theorem to determine for which primes $p$, $-50$ is a quadratic residue modulo $p$.
b) Use the Law of Quadratic Reciprocity and the Chinese Remainder Theorem to determine when $6$ is a quadratic residue modulo $p$.
So for (a), you'd say that $-50$ is a quadratic residue $\text{mod}$ $p$ if there exists an integer, say $x$, such that $x^2 \equiv(-50) \text{mod } p$.
I'm not exactly sure how to proceed from here. Any pointers?