"Let p = a prime. Show ≡ a (mod ) has 0 solutions if ≡ a (mod p) has 0 solutions, or 2 solutions if ≡ a (mod p) has 2."
I thought I should use Euler's criterion for this(?), which says ≡ if and only if ≡ 1 (mod p), but I don't know where to go from there.
Also, I know that a (mod p) can have only either exactly two solutions or zero solutions (by Lagrange), so the question remains how to map a (mod p) to a (mod )