Positive integer solutions of certain diophantine equations

Proceedings of the Indian Academy of Sciences. Mathematical sciences

BIJAN KUMAR PATEL^1¹  MANASI K SAHUKAR^3²  PRASANTA KUMAR RAY^2³ 

[1] International Institute of Information Technology, Bhubaneswar 751 003, India^1;National Institute of Technology, Rourkela 769 008, India^3;VSS University of Technology, Odisha, Burla 768 019, India^2

关键词: Diophantine equations;    balancing numbers;    balancers;    Lucas balancing numbers;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

In this study, the diophantine equations $x^{2} − 32B_{n}xy − 32y^{2} = \pm32^{r}, x^{4} − 32B_{n}xy − 32y^{2} = \pm32^{r}$ and $x^{2} − 32B_{n}xy − 32y^{4} = \pm32^{r}$ are considered and determined when these equations have positive integer solutions. Moreover, all positive integer solutions of these diophantine equations in terms of balancing and Lucas-balancing numbers are also found out.

【 授权许可】

CC BY