**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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## 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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## 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.