---
tag: 01G1WY1GVX
kind: definition
name: Pythagorean triple
msc: [11D09]
defines: 0M7ARED5Q7
uses: [02WF878BH1]
sources:
  - url: https://en.wikipedia.org/wiki/Pythagorean_triple
    locator: lead section
---

## Definition

A Pythagorean triple is a triple $(a, b, c)$ of positive integers such that $a^2 + b^2 = c^2$.
The triple is primitive if $\gcd(a, b, c) = 1$, with $\gcd$ the [[greatest common divisor|02WF878BH1]].

## Remarks

The smallest examples are $(3, 4, 5)$ and $(5, 12, 13)$.
If $(a, b, c)$ is a Pythagorean triple, then so is $(ka, kb, kc)$ for each positive integer $k$.
The [[classification of Pythagorean triples|0KF3J2KAER]] lists all of them.
In a primitive triple, $a$, $b$ and $c$ are pairwise coprime, and exactly one of $a$ and $b$ is even.

## Explanations

### L1 human

A Pythagorean triple gives a right triangle whose three sides are whole numbers.
The triangle with sides $3$, $4$ and $5$ is the best-known example, since $9 + 16 = 25$.