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}}
