# Pythagorean triple

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## Definition[edit]

A **Pythagorean triple** is a solution of the
equation , in which ,
and are positive integers.

A Pythagorean triple is called *primitive*, if .

## Properties[edit]

All primitive Pythagorean triples are given by:

where and are relatively-prime positive integers, and .

Every non-primitive Pythagorean triple a positive integer multiple of a primitive triple. These may also be generated by including relatively-prime integers for and .

## External references[edit]

- MathWorld's article
- Cut-the-knot's article