Pell equations and Pythagorean triples

Amra Duraković, Bernadin Ibrahimpašić

Pell's equation is any Diophantine equation of the form $x^2-Dy^2=1$, where $D$ is a given nonsquare positive integer and integer solutions are sought for $x$ and $y$. A Pythagorean triple is a triple of positive integers $a$, $b$ and $c$ such that a right triangle exists with legs $a$ and $b$, and hypotenuse $c$. In this paper we describe Pell's equations and their relation to the Pythagorean triples.