Searching Solutions With Renowned Numbers For Restricted Quadratic Diophantine Equations

Authors

  • V. Pandichelvi Assistant Professor, PG & Research Department of Mathematics, UrumuDhanalakshmi College, Trichy. (Affiliated to Bharathidasan University)
  • S. Saranya Research Scholar, PG & Research Department of Mathematics, UrumuDhanalakshmi College, Trichy. (Affiliated to Bharathidasan University)

Keywords:

quadratic Diophantine equation, Pell number, Half companion number.

Abstract

Objectives: Quadratic Diophantine equations with two variables or more than two variables are substantial area of current research. In the past review of literature, many authors discovered infinite number of integer solutions to enormous number of Binary quadratic Diophantine equations by reducing the considered equations to Pythagorean equations, Pell equations or other equations whose solutions are already offered. The objective of this article is to develop non-negative integer solutions to certain quadratic Diophantine equations consisting two variablesin terms of Pell and Half companion numbers by using the principle of mathematical induction.Additionally, the solutions of each equationare certified with the assistant of Python programs. Method: Diophantine equations may have infinite number of solutions or finite number of solutions or no solutions in integers. There is no commontechnique for resolving Diophantine equations. In this paper, quadratic Diophantine equations with two unknowns are solved by utilizing the principle of mathematical induction. Results and discussion: A limited number of quadratic Diophantine equations consisting two unknowns are investigated for finding solutions in terms of Pell and Half companion numbers by using the principle of mathematical induction. Moreover, all such exposed solutions are attested by different Python programs with slight modifications. Novelty: The derived solutions can be customized for any resultant Pell and Half companion sequencesandforall values of

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Published

2023-10-25

How to Cite

V. Pandichelvi, & S. Saranya. (2023). Searching Solutions With Renowned Numbers For Restricted Quadratic Diophantine Equations. Chinese Journal of Computational Mechanics, (5), 546–551. Retrieved from http://jslxxb.cn/index.php/jslxxb/article/view/4399

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