# Pythagorean n-tuple

Let $n\ge 3$ be an integer. A *Pythagorean n-tuple* is an n-tuple of integers $({x}_{1},\mathrm{\dots},{x}_{n})$
for which

$$\sum _{i=1}^{n-1}x_{i}{}^{2}=x_{n}{}^{2}.$$ |

It is said to be if $\mathrm{gcd}({x}_{1},\mathrm{\dots},{x}_{n})=1.$

If $n=3$ the 3-tuple is called a Pythagorean triplet or Pythagorean triple.

Title | Pythagorean n-tuple |
---|---|

Canonical name | PythagoreanNtuple |

Date of creation | 2013-03-22 16:55:58 |

Last modified on | 2013-03-22 16:55:58 |

Owner | Mathprof (13753) |

Last modified by | Mathprof (13753) |

Numerical id | 7 |

Author | Mathprof (13753) |

Entry type | Definition |

Classification | msc 11-00 |

Defines | primitive Pythagorean n-tuple |