Take a look at this problem. The Quadratic Reciprocity

Let p be an odd prime p > 3. What is (-2/p)?

This is Legendre symbol. (n/p) = 1 if n is a quadratic residue mod p
= -1 if n is quadratic non-residue mod p
= if p|n
n is a quadratic residue mod p if n= x^2 mod p for some integer x.

I understand that a little bit but I am having a hard time with how to start my proof.