Quadratic Reciprocity Theorem
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Quadratic reciprocity is a classic result of number theory. It is one of the most important theorem's in the study of quadratic residues.
It states that for primes
and
greater than
where both are not of the form
for some integer
.
If both
and
are of the form
, then
Another way to state this is: \left(\frac{p}{q}\right)\left(\frac{q}{p}\right)=(-1)^{\frac{p-1}{2}\frac{q-1}{2}}