• Positive Integer Solutions of the Diophantine Equation $x^2 - L_n xy + (-1)^n y^2 = \pm 5^r$

• Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/124/03/0301-0313

• Keywords

Fibonacci numbers; Lucas numbers; diophantine equations

• Abstract

In this paper, we consider the equation $x^2-L_n xy+(-1)^n y^2=\pm 5^r$ and determine the values of 𝑛 for which the equation has positive integer solutions 𝑥 and 𝑦. Moreover, we give all positive integer solutions of the equation $x^2-L_n xy+(-1)^n y^2=\pm 5^r$ when the equation has positive integer solutions.

• Author Affiliations

1. Sakarya University, Merkezi, 54180 Sakarya, Turkey
2. Bingöl University, Rektörlüğü, 12000 Bingöl, Turkey

• Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 3
June 2019