# Euler’s criterion

Let $p$ be an odd prime and $n$ an integer such that $(n,p)=1$ (that is, $n$ and $p$ are relatively prime).

Then $(n|p)\equiv {n}^{(p-1)/2}(modp)$ where $(n|p)$ is the Legendre symbol^{}.

Title | Euler’s criterion |

Canonical name | EulersCriterion |

Date of creation | 2013-03-22 12:20:00 |

Last modified on | 2013-03-22 12:20:00 |

Owner | drini (3) |

Last modified by | drini (3) |

Numerical id | 5 |

Author | drini (3) |

Entry type | Theorem |

Classification | msc 11A15 |

Related topic | GaussLemma |

Related topic | QuadraticReciprocityRule |

Related topic | LegendreSymbol |

Related topic | QuadraticResidue |

Related topic | ProofOfGaussLemma |

Related topic | PropertiesOfTheLegendreSymbol |

Related topic | 1IsQuadraticResidueIfAndOnlyIfPequiv1Mod4 |