: Mathematics: Pythagorean quadruple

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Pythagorean quadruple

A Pythagorean quadruple is a tuple of integers $a$ , $b$ , $c$ , and $d$ , such that $a 2 + b 2 + c 2 = d 2$ . They are solutions of a Diophantine equation and often only positive integer values are considered. However, to provide a more complete geometric interpretation, the integer values can be allowed to be negative and zero (thus allowing Pythagorean triples to be included) with the only condition being that $d > 0$ . In this setting, a Pythagorean quadruple $(a, b, c, d)$ defines a cuboid with integer side lengths $| a |$ , $| b |$ , and $| c |$ , whose space diagonal has integer length $d$ ; with this interpretation, Pythagorean quadruples are thus also called Pythagorean boxes. In this article we will assume, unless otherwise stated, that the values of a Pythagorean quadruple are all positive integers.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Pythagorean_quadruple)

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