---
tag: 1NN95HE6DY
kind: concept
name: Legendre
sources:
  - wikipedia: en:73634@r1376316324
    locator: Glossary of mathematical symbols, section Brackets > Parentheses
    note: adopted
    mention: wikipedia://en/73634#FMMG
    sections: [Summary]
inventory: [VE22MCZ2C7]
---

## Summary

[[Legendre symbol|01J8AMV9RS]]: If $p$ is an odd [[prime number|01826KMG2H]] and $a$ is an [[integer|0C4JS9RF5M]], the value of $\left(\frac{a}{p}\right)$ is $1$ if $a$ is a [[quadratic residue|0DKCECSYCF]] modulo $p$; it is $-1$ if $a$ is a quadratic non-residue modulo $p$; it is $0$ if $p$ divides $a$. The same notation is used for the [[Jacobi symbol|0ADTQBXRMC]] and Kronecker symbol, which are generalizations where $p$ is respectively any odd positive integer, or any integer.