Math 2.0

Number theory Definition

Pythagorean triple

Builds on Greatest common divisor

Definition

A Pythagorean triple is a triple (a,b,c)(a, b, c) of positive integers such that a2+b2=c2a^2 + b^2 = c^2. The triple is primitive if gcd⁡(a,b,c)=1\gcd(a, b, c) = 1, with gcd⁡\gcd the greatest common divisor.

Remarks

The smallest examples are (3,4,5)(3, 4, 5) and (5,12,13)(5, 12, 13). If (a,b,c)(a, b, c) is a Pythagorean triple, then so is (ka,kb,kc)(ka, kb, kc) for each positive integer kk. The classification of Pythagorean triples lists all of them. In a primitive triple, aa, bb and cc are pairwise coprime, and exactly one of aa and bb is even.

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Further reading

  1. Web https://en.wikipedia.org/wiki/Pythagorean_triple, lead section
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