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
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Authors and affiliations

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


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.


  • Parametrization of primitive solutions

2010 Mathematics Subject Classification

  • 11D09


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Cite this paper


Chang, S. (2019). Direct parametrization of Pythagorean triples. Notes on Number Theory and Discrete Mathematics, 25(3), 21-35, doi: 10.7546/nntdm.2019.25.3.21-35.


Chang, Sungkon. “Direct Parametrization of Pythagorean Triples.” Notes on Number Theory and Discrete Mathematics 25, no. 3 (2019): 21-35, doi: 10.7546/nntdm.2019.25.3.21-35.


Chang, Sungkon. “Direct Parametrization of Pythagorean Triples.” Notes on Number Theory and Discrete Mathematics 25.3 (2019): 21-35. Print, doi: 10.7546/nntdm.2019.25.3.21-35.

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