Pell Equations and Pythagorean Triples with Constant Difference of Two Legs

A Pythagorean triple is composed of a pair of legs a, b and a hypotenuse c, where a, b, c are positive integers. For a given positive integer q, the group of Pythagorean triples whose legs have difference q is called the dq group by H. Hosoya [3]. In the present paper, using some results about Pell equation, we investigate extensively the structure of dq group.