Difference between revisions of "Quadratic Reciprocity Theorem"

Revision as of 11:23, 30 May 2019

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 $\left(\frac{p}{q}\right)= \left(\frac{q}{p}\right)$ for primes $p$ and $q$ greater than $2$ where both are not of the form $4n+3$ for some integer $n$ .
If both $p$ and $q$ are of the form $4n+3$ , then $\left(\frac{p}{q}\right)= -\left(\frac{q}{p}\right).$