Primitive Pythagorean Triples With The Difference Of The Right Sides Is A Perfect Square

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Natural and Applied Sciences Journal
Cilt: 8 Sayı: 2
Primitive Pythagorean Triples With The Difference Of The Right Sides Is A Perfect Square

Primitive Pythagorean Triples With The Difference Of The Right Sides Is A Perfect Square

Authors : Murat Alan, Derya Mazineler

Pages : 22-27

Doi:10.38061/idunas.1711231

View : 42 | Download : 137

Publication Date : 2025-12-31

Article Type : Research Paper

Abstract :Let (x,y,z) be a primitive Pythagorean triples such that x^2+y^2=z^2 with gcd⁡(x,y,z)=1. In this paper, we search all primitive Pythagorean triples such that the difference of its right sides is a perfect square. We show that there are infinitely many such Pythagorean triples. In fact, we give the parametric equation of all sides of such Pythagorean triples depending on two parameters. To get the results, we use some elementary methods as well as generalized Pell equations and some classical Diophantine Equations from number theory.
Keywords : Pisagor üçlüleri, Diofant denklemler, Pell denklemi

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