Congruent Numbers Via the Pell Equation and its Analogous Counterpart

2010/04/02 by Farzali Izadi, Izadi, Farzali
Mathematics · #14H52 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #G.2.0 #History and Overview (math.HO) #Mathematics and Applications #Number Theory (math.NT) #Primary: 11D09 #Secondary: 11E16 #acm:11D09 #acm:11E16 #acm:14H52 #math.HO #math.NT #msc:11D09 #msc:11E16 #msc:14H52

paper · pdf · doi:10.48550/arxiv.1004.0261

8 pages

openalex publication_date 2010/04/02 · arxiv created 2010/12/30 · arxiv updated 2011/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 x²-dy²=1 plus its analogous counterpart x²-dy²=-1 which give rise to congruent numbers n with arbitrarily many prime factors.

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