# Wilson’s theorem result

The following is a variant of Wilson’s theorem:

Let $p$ be a positive integer and $1\le k\le p-1$. Then:

$p$ is prime if and only if

$$(p-k)!(k-1)!\equiv {(-1)}^{k}\phantom{\rule{veryverythickmathspace}{0ex}}(modp).$$ |

For particular $k=1,2,\mathrm{\dots}$ one gets nice results.

Title | Wilson’s theorem result |
---|---|

Canonical name | WilsonsTheoremResult |

Date of creation | 2013-03-22 14:20:44 |

Last modified on | 2013-03-22 14:20:44 |

Owner | mathwizard (128) |

Last modified by | mathwizard (128) |

Numerical id | 6 |

Author | mathwizard (128) |

Entry type | Result |

Classification | msc 11-00 |