On the Diophantine Equation $x^2 - kxy + ky^2 + 3^ny = 0, n = 1, 2, 3$

Supawadee Prugsapitak; Nattaporn Thongngam

On the Diophantine Equation $x^2 - kxy + ky^2 + 3^ny = 0, n = 1, 2, 3$

Authors

Supawadee Prugsapitak Prince of Songkla University
Nattaporn Thongngam

Keywords:

Diophantine equation, Pell equation, quadratic Diophantine equation

Abstract

In this article, we determine all values of $k$ when the equation $x^2 - kxy + ky^2 + 3^ny = 0$ where $n = 1, 2, 3$ has infinitely many positive solutions.

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Published

2024-12-20

How to Cite

Prugsapitak, S., & Thongngam, N. (2024). On the Diophantine Equation $x^2 - kxy + ky^2 + 3^ny = 0, n = 1, 2, 3$. Thai Journal of Mathematics, 22(3), 503–508. Retrieved from https://thaijmath2.in.cmu.ac.th/index.php/thaijmath/article/view/1512