# exactly divides

Let $a$ and $b$ be integers and $n$ a positive integer. Then ${a}^{m}$ *exactly divides* $b$ (denoted as ${a}^{n}\parallel n$) if ${a}^{n}$ divides $b$ but ${a}^{n+1}$ does not divide $b$. For example, ${2}^{4}\parallel 48$.

One can, of course, use the similar expression and notation for the elements $a$, $b$ of any commutative ring or monoid (cf. e.g. divisor as factor of principal divisor).

Title | exactly divides |
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Canonical name | ExactlyDivides |

Date of creation | 2013-03-22 16:10:44 |

Last modified on | 2013-03-22 16:10:44 |

Owner | Wkbj79 (1863) |

Last modified by | Wkbj79 (1863) |

Numerical id | 7 |

Author | Wkbj79 (1863) |

Entry type | Definition |

Classification | msc 11A51 |

Related topic | Divides |

Related topic | Divisibility |

Related topic | DivisibilityInRings |