A basis of the group of primitive almost pythagorean triples

2014/01/13 by Nikolai A. Krylov, Krylov, Nikolai A.
Mathematics · #11R04 #11R11 #20F05 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11R04 #msc:11R11 #msc:20F05

paper · pdf · doi:10.48550/arxiv.1401.2869

10 pages, continuation of arXiv:1107.2860

arxiv created 2014/01/13 · arxiv updated 2014/01/14

Abstract

Let m be a fixed square-free positive integer, then equivalence classes of solutions of Diophantine equation x²+m⋅ y²=z² form an infinitely generated abelian group under the operation induced by the complex multiplication. A basis of this group is constructed here using prime ideals and the ideal class group of the field \mathbb Q (√(-m)).

Citations

• The Group of Primitive Almost Pythagorean Triples

Related

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• Class Numbers and Pell's Equation x² + 105y² = z²
• Connections of Class Numbers to the Group Structure of Generalized Pythagorean Triples
• On the subgroup generated by solutions of Pell's equation
• A Note on Generating Almost Pythagorean Triples