# Bezout’s lemma (number theory)

Let $a,b$ be integers, not both zero. Then there exist two integers $x,y$ such that:

$$ax+by=\mathrm{gcd}(a,b).$$ |

This does not only work on $\mathbb{Z}$ but on every integral domain where an Euclidean valuation has been defined.

Title | Bezout’s lemma (number theory^{}) |
---|---|

Canonical name | BezoutsLemmanumberTheory |

Date of creation | 2013-03-22 12:40:40 |

Last modified on | 2013-03-22 12:40:40 |

Owner | mathwizard (128) |

Last modified by | mathwizard (128) |

Numerical id | 10 |

Author | mathwizard (128) |

Entry type | Theorem |

Classification | msc 11A05 |

Synonym | Bezout’s lemma |

Synonym | Bezout’s theorem |

Related topic | EuclidsAlgorithm |

Related topic | EuclidsCoefficients |

Related topic | GreatestCommonDivisorOfSeveralIntegers |