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

James D. Shaw, James Guyker and Sergejs Solovjovs

International Journal of Mathematics and Mathematical Sciences, 2023, vol. 2023, 1-18

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.

Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:1505337

DOI: 10.1155/2023/1505337

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