# Pythagorean n-tuple

Let $n\geq 3$ be an integer. A Pythagorean n-tuple is an n-tuple of integers $(x_{1},\ldots,x_{n})$ for which

 $\sum_{i=1}^{n-1}{x_{i}}^{2}={x_{n}}^{2}.$

It is said to be if $\mathrm{gcd}(x_{1},\ldots,x_{n})=1.$

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

Title Pythagorean n-tuple PythagoreanNtuple 2013-03-22 16:55:58 2013-03-22 16:55:58 Mathprof (13753) Mathprof (13753) 7 Mathprof (13753) Definition msc 11-00 primitive Pythagorean n-tuple