Pythagorean triple

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.

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 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 $9 + 16 = 25$.