Pythagorean triples: Difference between revisions

A [[wp:Pythagorean_triple|Pythagorean triple]] is defined as three positive integers <math>(a, b, c)</math> where <math>a\leq < b\leq < c</math>, and <math>a^2+b^2=c^2.</math> They are called primitive triples if <math>a, b, c</math> are coprime, that is, if their pairwise greatest common divisors <math>{\rm gcd}(a, b) = {\rm gcd}(a, c) = {\rm gcd}(b, c) = 1</math>. Because of their relationship through the Pythagorean theorem, a, b, and c are coprime if a and b are coprime (<math>{\rm gcd}(a, b) = 1</math>). Each triple forms the length of the sides of a right triangle, whose perimeter is <math>P=a+b+c</math>.