Q:

Question involving Legendre symbols

Let r,p,q be distinct odd primes. Let 4r divide p-q. Show that
(r/p) = (r/q)
Where (a/b) is the Legendre symbol.
I'm sure we are suppose to use the law of quadratic reciprocity. I don't think this question is suppose to be difficult, but I cannot figure it out!

A:

Hint:
$$4r\mid (p-q)\iff p\equiv q\bmod r\quad\text{and}\quad p\equiv q\bmod 4$$

