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

Yasuaki Gyoda

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