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 $\gcd (x_1,\mathrm{\dots },x_n)=1.$

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