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