Quadratic Reciprocity Theorem

Quadratic reciprocity is a classic result of number theory.
It is one of the most important theorems in the study of quadratic residues.

Statement

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:

• Note that is [b]not[/b] a fraction. It is the [b]Legendre notation[/b] of quadratic residuary.