# divisibility

Given integers $a$ and $b$, then we say $a$ *divides* $b$ if and only if there is some $q\in \mathbb{Z}$ such that $b=qa$.

There are many other ways in common use to express this relationship:

The notion of divisibility can apply to other rings (e.g., polynomials).

Title | divisibility |

Canonical name | Divisibility |

Date of creation | 2013-03-22 11:59:49 |

Last modified on | 2013-03-22 11:59:49 |

Owner | mathcam (2727) |

Last modified by | mathcam (2727) |

Numerical id | 11 |

Author | mathcam (2727) |

Entry type | Definition |

Classification | msc 11A51 |

Synonym | divides |

Synonym | divisor |

Synonym | factor |

Synonym | multiple |

Related topic | LeastCommonMultiple |

Related topic | ExampleOfGcd |

Related topic | TauFunction |

Related topic | ExactlyDivides |

Related topic | DivisorSumOfAnArithmeticFunction |

Related topic | StrictDivisibility |

Related topic | FundamentalTheoremOfArithmetic |

Related topic | NumberTheory |