# radical of an integer

Given a natural number^{} $n$, let $n={p}_{1}^{{\alpha}_{1}}\mathrm{\cdots}{p}_{k}^{{\alpha}_{k}}$ be its unique factorization^{} as a product^{} of distinct prime powers. Define the of $n$, denoted $\text{rad}(n)$, to be the product ${p}_{1}\mathrm{\cdots}{p}_{k}$. The radical^{} of a square-free number is itself.

Title | radical of an integer |

Canonical name | RadicalOfAnInteger |

Date of creation | 2013-03-22 11:45:21 |

Last modified on | 2013-03-22 11:45:21 |

Owner | KimJ (5) |

Last modified by | KimJ (5) |

Numerical id | 12 |

Author | KimJ (5) |

Entry type | Definition |

Classification | msc 13A10 |

Classification | msc 81-00 |

Classification | msc 18-00 |

Synonym | square-free part |

Related topic | RadicalOfAnIdeal |

Related topic | PowerOfAnInteger |

Defines | radical |