# Definitions for **Pythagorean triple**

### This page provides all possible meanings and translations of the word **Pythagorean triple**

### Wiktionary

Pythagorean triple(ProperNoun)

A set of three positive integers a, b and c, where a = b + c

### Freebase

Pythagorean triple

A Pythagorean triple consists of three positive integers a, b, and c, such that a² + b² = c². Such a triple is commonly written, and a well-known example is. If is a Pythagorean triple, then so is for any positive integer k. A primitive Pythagorean triple is one in which a, b and c are coprime. A right triangle whose sides form a Pythagorean triple is called a Pythagorean triangle. The name is derived from the Pythagorean theorem, stating that every right triangle has side lengths satisfying the formula a² + b² = c²; thus, Pythagorean triples describe the three integer side lengths of a right triangle. However, right triangles with non-integer sides do not form Pythagorean triples. For instance, the triangle with sides a = b = 1 and c = √2 is right, but is not a Pythagorean triple because √2 is not an integer. Moreover, 1 and √2 do not have an integer common multiple because √2 is irrational.

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"Pythagorean triple." *Definitions.net.* STANDS4 LLC, 2014. Web. 3 Sep. 2014. <http://www.definitions.net/definition/Pythagorean triple>.