# Giuga number

A *Giuga number* is a squarefree^{} composite number^{} $n$ such that each prime factor^{} ${p}_{i}|(\frac{n}{{p}_{i}}-1)$. For these numbers it then follows that $n{B}_{\varphi (n)}\equiv -1modn$, (where ${B}_{x}$ is a Bernoulli number^{}).

The first few Giuga numbers are 30, 858, 1722, 66198, 2214408306, 24423128562 (listed in sequence A007850 of Sloane’s OEIS).

All known Giuga numbers are even and have at least three factors. An odd Giuga number would have to have at least twelve factors.

Title | Giuga number |
---|---|

Canonical name | GiugaNumber |

Date of creation | 2013-03-22 15:50:22 |

Last modified on | 2013-03-22 15:50:22 |

Owner | Mravinci (12996) |

Last modified by | Mravinci (12996) |

Numerical id | 7 |

Author | Mravinci (12996) |

Entry type | Definition |

Classification | msc 11D85 |

Related topic | PrimaryPseudoperfectNumber |