# squarefull number

A natural number $n$ is called squarefull (or powerful) if for every prime $p|n$ we have ${p}^{2}|n$. In 1978 ErdÅ‘s conjectured that we cannot have three consecutive squarefull natural numbers. If we assume the ABC Conjecture^{}, there are only finitely many such consecutive triples.

Title | squarefull number |

Canonical name | SquarefullNumber |

Date of creation | 2013-03-22 11:45:26 |

Last modified on | 2013-03-22 11:45:26 |

Owner | KimJ (5) |

Last modified by | KimJ (5) |

Numerical id | 10 |

Author | KimJ (5) |

Entry type | Definition |

Classification | msc 11A51 |

Classification | msc 55-00 |

Classification | msc 82-00 |

Classification | msc 83-00 |

Classification | msc 81-00 |

Classification | msc 39A99 |

Classification | msc 39B72 |

Classification | msc 33E30 |

Synonym | powerful number |

Related topic | NFullNumber |