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.
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 not a fraction. It is the Legendre notation of quadratic residuary.