ON SOLUTIONS OF THE DIOPHANTINE EQUATION
For the Diophantine equation where and are the Pell-Lucas numbers, we find all the non-negative integral solutions in By using the theory of linear forms in logarithms of algebraic numbers, we derive an explicit upper bound for and then, by reduction method based on continued fraction algorithm, we achieve our objective.
Pell-Lucas numbers, Diophantine equation, algebraic numbers.
Received: January 12, 2022; Accepted: March 27, 2022; Published: May 12, 2022
How to cite this article: Priyanka Relhan and Vipin Verma, On solutions of the Diophantine equation , JP Journal of Algebra, Number Theory and Applications 55 (2022), 9-21. http://dx.doi.org/10.17654/0972555522016
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
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