The group of primitive Pythagorean triples over Gaussian integers

Attawut Wongpradit; Ekkasit Sangwisut

doi:10.1016/j.heliyon.2023.e16747

The group of primitive Pythagorean triples over Gaussian integers

Heliyon. 2023 Jun 1;9(6):e16747. doi: 10.1016/j.heliyon.2023.e16747. eCollection 2023 Jun.

Authors

Attawut Wongpradit¹, Ekkasit Sangwisut²

Affiliations

¹ Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University (Rangsit Center), Pathum Thani 12120, Thailand.
² Department of Mathematics and Statistics, Faculty of Science, Thaksin University, Phattalung 93110, Thailand.

Abstract

A group structure of the set of primitive Pythagorean triples over Gaussian integers is investigated. In addition, we show that it is a free abelian group. Base on the study, the construction and enumeration of the primitive Pythagorean triples having the same hypotenuse are established.

Keywords: Free abelian group; Gaussian integers; Pythagorean triple.