# quadratic residue

Let $a,n$ be relatively prime integers. If there exists an integer $x$ that satisfies

$${x}^{2}\equiv a\phantom{\rule{veryverythickmathspace}{0ex}}(modn)$$ |

then $a$ is said to be a *quadratic residue ^{}* of $n$. Otherwise, $a$ is called a

*quadratic nonresidue*of $n$.

Title | quadratic residue |
---|---|

Canonical name | QuadraticResidue |

Date of creation | 2013-03-22 11:55:19 |

Last modified on | 2013-03-22 11:55:19 |

Owner | mathcam (2727) |

Last modified by | mathcam (2727) |

Numerical id | 9 |

Author | mathcam (2727) |

Entry type | Definition |

Classification | msc 11A15 |

Related topic | LegendreSymbol |

Related topic | EulersCriterion |

Defines | quadratic non-residue |

Defines | quadratic nonresidue |