Glasnik Matematicki, Vol. 56, No. 2 (2021), 263-270. \( \)

ON THE RAMANUJAN-NAGELL TYPE DIOPHANTINE EQUATION \(Dx^2+k^n=B\)

Zhongfeng Zhang and Alain Togbé

School of Mathematics and Statistics, Zhaoqing University, Zhaoqing 526061, China
e-mail:bee2357@163.com

Department of Mathematics and Statistics, Purdue University Northwest, 1401 S. U.S. 421 Westville, IN 46391, USA
e-mail:atogbe@pnw.edu

Abstract.   In this paper, we prove that the Ramanujan-Nagell type Diophantine equation \(Dx^2+k^n=B\) has at most three nonnegative integer solutions \((x, n)\) for \(k\) a prime and \(B, D\) positive integers.

2020 Mathematics Subject Classification.   11D41, 11D61

Key words and phrases.   Diophantine equation, Pell equations.

https://doi.org/10.3336/gm.56.2.04

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