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

Proceedings Mathematical Sciences

Zafer Åžiar¹  Refik Keskin² 

[1] Bingöl University, Rektörlüğü, 000 Bingöl, Turkey$$;Sakarya University, Merkezi, 0 Sakarya, Turkey$$

关键词: Fibonacci numbers;    Lucas numbers;    diophantine equations;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

In this paper, we consider the equation $x^2-L_n xy+(-1)^n y^2=± 5^r$ 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 $x^2-L_n xy+(-1)^n y^2=± 5^r$ when the equation has positive integer solutions.

【 授权许可】

Unknown