On Parametric and Matrix Solutions to the Diophantine Equation x2+dy2−z2=0 Where d Is a Positive Square‐Free Integer

Abstract

The well‐known matrix‐generated tree structure for Pythagorean triplets is extended to the primitive solutions of the Diophantine equation x2+dy2−z2=0 where d is a positive square‐free integer. The proof is based on a parametrization of these solutions as well as on a dual version of the Fermat’s method of descent.