高斯整数上的本原毕达哥拉斯三元数组群。

The group of primitive Pythagorean triples over Gaussian integers.

作者信息

Wongpradit Attawut, Sangwisut Ekkasit

机构信息

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

Department of Mathematics and Statistics, Faculty of Science, Thaksin University, Phattalung 93110, Thailand.

出版信息

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

DOI:10.1016/j.heliyon.2023.e16747

PMID:37346328

原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC10279819/

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.

摘要

研究了高斯整数上本原毕达哥拉斯三元数组集的群结构。此外，我们证明它是一个自由阿贝尔群。基于该研究，建立了具有相同斜边的本原毕达哥拉斯三元数组的构造与枚举。