Congruent numbers via the Pell equation and its analogous counterpart

Farzali Izadi
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 21, 2015, Number 1, Pages 70–78
Full paper (PDF, 154 Kb)

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Authors and affiliations

Farzali Izadi
Department of Mathematics, Azarbaijan Shahid Madani University
Tabriz, Iran

Abstract

The aim of this article is twofold. The first aim consists of introducing several polynomials of one variable as well as two variables defined on the positive integers with values as congruent numbers. The second aim is to present connections between Pythagorean triples and the Pell equation x² − dy² = 1 plus its analogous counterpart x² − dy² = − 1 which give rise to congruent numbers n with arbitrarily many prime factors.

Keywords

• Congruent numbers
• Pell equations
• Pythagorean triples
• Diophantine equations
• Elliptic curves

AMS Classification

• Primary: 11D09
• Secondary: 11E16, 14H52

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