Positive integer solutions to $(x+y)^2+(y+z)^2+(z+x)^2=12xyz$
Number Theory
2022-09-20 v4 Combinatorics
Abstract
In this paper, we give a specific way of describing positive integer solutions of a Diophantine equation and introduce a generalized cluster pattern behind it.
Cite
@article{arxiv.2109.09639,
title = {Positive integer solutions to $(x+y)^2+(y+z)^2+(z+x)^2=12xyz$},
author = {Yasuaki Gyoda},
journal= {arXiv preprint arXiv:2109.09639},
year = {2022}
}
Comments
Addition of Remark 1.4, which explain the history of discovering of Theorem 1.1, correction of the equation (3.2), replacement of Example 3.7, 3.11 to be related to Example 3.6, 14 pages