Direct parametrization of Pythagorean triples

Sungkon Chang, Department of Mathematics, Georgia Southern University
2019 Notes on Number Theory and Discrete Mathematics  
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.
doi:10.7546/nntdm.2019.25.3.21-35 fatcat:z43cyd25ujgwjbbwejewn7a76u