Positive integer solutions to $(x+y)^2+(y+z)^2+(z+x)^2=12xyz$

Yasuaki Gyoda

paper

Positive integer solutions to $(x + y)^{2} + (y + z)^{2} + (z + x)^{2} = 12 x y z$

arXiv:2109.09639

Abstract

In this paper, we give a specific way of describing positive integer solutions of a Diophantine equation $(x + y)^{2} + (y + z)^{2} + (z + x)^{2} = 12 x y z$ and introduce a generalized cluster pattern behind it.

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

Positive integer solutions to (x+y)2+(y+z)2+(z+x)2=12xyz

Abstract

Positive integer solutions to $(x + y)^{2} + (y + z)^{2} + (z + x)^{2} = 12 x y z$