On Parametric and Matrix Solutions to the Diophantine Equation $x^{2} + d y^{2} - z^{2} = 0$ Where $d$ Is a …

IF 1 Q1 MATHEMATICS INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES Pub Date : 2023-09-25 DOI:10.1155/2023/1505337

James D. Shaw, James Guyker

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引用次数: 0

Abstract

The well‐known matrix‐generated tree structure for Pythagorean triplets is extended to the primitive solutions of the Diophantine equation

x^{2} + d y^{2} - z^{2} = 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.

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Diophantine方程x 2 + d y 2−z 2 = 0的参数解和矩阵解

众所周知，毕达哥拉斯三元组的矩阵生成树形结构被推广到丢芬图方程x2 + d2 - z2 = 0的原始解中，其中d是一个正的无平方整数。证明是基于这些解的参数化以及费马下降法的对偶版本。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES Mathematics-Mathematics (miscellaneous)

CiteScore

2.30

自引率

8.30%

发文量

审稿时长

17 weeks

期刊介绍： The International Journal of Mathematics and Mathematical Sciences is a refereed math journal devoted to publication of original research articles, research notes, and review articles, with emphasis on contributions to unsolved problems and open questions in mathematics and mathematical sciences. All areas listed on the cover of Mathematical Reviews, such as pure and applied mathematics, mathematical physics, theoretical mechanics, probability and mathematical statistics, and theoretical biology, are included within the scope of the International Journal of Mathematics and Mathematical Sciences.

On Parametric and Matrix Solutions to the Diophantine Equation x 2 + d y 2 − z 2 = 0 Where d Is a …

Abstract

On Parametric and Matrix Solutions to the Diophantine Equation $x^{2} + d y^{2} - z^{2} = 0$ Where $d$ Is a …