English

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 (x+y)2+(y+z)2+(z+x)2=12xyz(x+y)^2+(y+z)^2+(z+x)^2=12xyz and introduce a generalized cluster pattern behind it.

Keywords

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