Congruent Numbers Via the Pell Equation and its Analogous Counterpart

Farzali Izadi

Congruent Numbers Via the Pell Equation and its Analogous Counterpart

History and Overview 2011-01-04 v4 Number Theory

Authors: Farzali Izadi

Abstract

The aim of this expository article is twofold. The first is to introduce several polynomials of one variable as well as two variables defined on the positive integers with values as congruent numbers. The second 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 equation Pythagorean triples polynomials prime factors

Cite

@article{arxiv.1004.0261,
  title  = {Congruent Numbers Via the Pell Equation and its Analogous Counterpart},
  author = {Farzali Izadi},
  journal= {arXiv preprint arXiv:1004.0261},
  year   = {2011}
}

Comments

8 pages

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