Farzali Izadi

Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132

Volume 21, 2015, Number 1, Pages 70—78

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## Details

### 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 *x*^{2} − *dy*^{2} = 1 plus its analogous counterpart *x*^{2} − *dy*^{2} = − 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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## Cite this paper

APAIzadi, F. (2015). Congruent numbers via the Pell equation and its analogous counterpart. Notes on Number Theory and Discrete Mathematics, 21(1), 70-78.

ChicagoIzadi, Farzali. “Congruent Numbers via the Pell Equation and Its Analogous Counterpart.” Notes on Number Theory and Discrete Mathematics 21, no. 1 (2015): 70-78.

MLAIzadi, Farzali. “Congruent Numbers via the Pell Equation and Its Analogous Counterpart.” Notes on Number Theory and Discrete Mathematics 21.1 (2015): 70-78. Print.