If $p$ & $q$ are distinct primes of the form $4K+3$ and $$x^2 \; \equiv \; p(\;mod \;q)$$ has no solution then prove that $$x^2 \; \equiv \; q(\;mod \;p)$$ has two solutions
I see that this statement somewhat resembles the Quadratic reciprocity theorem which goes in similar way that one of these congruence is solvable and other is not
How can I prove that the congruence has exactly two solutions