Definition:Legendre Symbol

Definition
Let $p$ be an odd prime.

Let $a \in \Z$ be an integer.

Definition 3
For a given $p$, the Legendre symbol is usually treated as a function $f_p: \Z \to \left\{{-1, 0, 1}\right\}$.

Also known as
The Legendre symbol for fixed prime $p$ is also known as the quadratic character modulo $p$.

Also see

 * Equivalence of Definitions of Legendre Symbol


 * Law of Quadratic Reciprocity
 * Euler's Criterion


 * Definition:Quadratic Residue
 * Definition:Quadratic Non-Residue


 * Properties of Legendre Symbol