q and p are odd primes.
They are not congruent mod4.
a isn't a divisor of p or q.

Prove quadratic reciprocity law hold for p and q, using

If q = +-p (mod4a) then (a|p) = (a|q).
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(... I think p = 4a - q (mod4) and q = 4a + p (mod4) ... but I think I'm missing something when I try to prove it...)