In 2017, the Diophantine equation  (_*) was preliminarily discussed [12]. The positive integer solutions of some equations derived from (_*) were solved, where p = 661. In this paper, this equation (_*) is further discussed and its results are supplemented. All the positive integer solutions of the remaining unsolved equations are solved by using simple and elementary methods, which are verified by computer calculation.

Diophantine equation, positive integer solution, greatest common divisor, prime number.

Received: April 17, 2022; Revised: May 10, 2022; Accepted: June 6, 2022; Published: July 1, 2022

How to cite this article: Xiaodan Yuan, A Diophantine equation and its positive integer solutions, JP Journal of Algebra, Number Theory and Applications 56 (2022), 37-69. http://dx.doi.org/10.17654/0972555522024

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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