A Geometrial Approach to the Diophantine Equation x12 + x22 + x32 + ... + xn2 = u2

Journal article

Authors/Editors

RATCHANIKORN CHONCHAIYA

Strategic Research Themes

Other (Strategic Research Themes)

Publication Details

Author list: Ratchanikorn Chonchaiya;Warin Vipismakul;Arisa Jiratampradab

Publication year: 2021

Volume number: 1370

Issue number: 3

Start page: 1364

End page: 1370

Number of pages: 7

ISSN: 16742370

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

Abstract

We find all Diophantine solutions for the equation x12 + x22 + x32 + ... + xn2 = u2 by geometrical approach from (Ayoub, 1984) to find solutions of the equation (Ayoub, 1984) to find solutions of the equation x2 + y2 + z2 = u2. We can find all rational points on theunit n-sphere by lines connecting those rational points to the point (1, 0 , ..., 0 ). Such linear parametric equations will always have rational slopes.

Keywords

ทรงกลมหนึ่งหน่วย มิติ, สมการไดโอแฟนไทน์, สามสิ่งอันดับพีทาโกรัส