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

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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.