Direct parametrization of Pythagorean triples

Sungkon Chang
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 25, 2019, Number 3, Pages 21–35
DOI: 10.7546/nntdm.2019.25.3.21-35
Full paper (PDF, 240 Kb)

Details

Authors and affiliations

Sungkon Chang
Department of Mathematics, Georgia Southern University, Armstrong Campus
11935 Abercorn St, Savannah GA, U.S.A.

Abstract

If the two axes of symmetry of a quadratic form in two variables have integer coefficients, the reflection across the axes defines a group action on the primitive solutions of the Diophantine equation defined by the quadratic form. In this paper, we introduce quadratic forms with rational axes of symmetry that admit a single set of polynomials which parametrize their primitive solutions up to the reflections.

Keywords

• Parametrization of primitive solutions

2010 Mathematics Subject Classification

• 11D09

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