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On Diophantine equation xª±b=Dy²
- 1 Guangzhou New Channel(Xinde Campus)
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Abstract
Diophantine equation is an important part of the number theory and it has been widely studied for a long time. There are many studies on solving the integral solutions of Diophantine equations using algebraic methods. This paper uses documentation method, sums up the results of research in different documents of finding the integral solutions of some Diophantine equations in various conditions, especially the utilization of theories on Pell equation, which in the form of xª±b=Dy². This paper mainly considers the situations when a =2 or a=3, which is a particular type of Diophantine equation. Several of the studies focus on the same equation but using different ways. Also, some subsequent studies on different equations are based on the former theorems provided by other writers and expand these theorems to broader applications. In order to emphasize the theorems obtained by the essays quoted and the methods the authors used, most of the mathematical procedures in their proofs are omitted.
Keywords
Diophantine Equation, Integral Solutions, Pell Equation, Algebra, Number Theory
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Cite this article
Song,J. (2023). On Diophantine equation xª±b=Dy². Theoretical and Natural Science,13,232-236.
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Volume title: Proceedings of the 3rd International Conference on Computing Innovation and Applied Physics
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