A Geometrical Approach to the Diophantine Equation x^{2}_{1}+x_{2}^{2}+x_{3}^{2}+...+x_{n}^{2}=u^{2}

Journal article

Authors/Editors

RATCHANIKORN CHONCHAIYA

Strategic Research Themes

Creative and Learning Society (Strategic Research Themes)

Publication Details

Author list: Ratchanikorn Chonchaiya, Warin Vipismakul and Arisa Jiratampradab

Publication year: 2021

Volume number: 26

Issue number: 3

Start page: 1364

End page: 1370

Number of pages: 7

ISSN: 2351-0781

URL: http://science.buu.ac.th/ojs246/index.php/sci/article/view/3471

Languages: English-United States (EN-US)

Abstract

We find all Diophantine solutions for the equation x^{2}_{1}+x_{2}^{2}+x_{3}^{2}+...+x_{n}^{2}=u^{2} by refining the geometrical approach from ( Ayoub, 1984) to find solutions of the equation x^{2}+y^{2}+z^{2}=u^{2} . We can find all rational points on the unit n-sphere by lines connecting those rational points to the point (1, 0, ..., 0 ). Such linear parametric equations will always have rational slopes.

Keywords

Diophantine solutions