Glasnik Matematicki, Vol. 53, No. 1 (2018), 43-50.

ON THE RAMANUJAN-NAGELL TYPE DIOPHANTINE EQUATION X2+AKN=B

Zhongfeng Zhang and Alain Togbé

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

Department of Mathematics, Statistics and Computer Science, 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 x2+Akn=B has at most three nonnegative integer solutions (x, n) for A=1, 2, 4, k an odd prime and B a positive integer. Therefore, we partially confirm two conjectures of Ulas from [23].

2010 Mathematics Subject Classification.   11D41.

Key words and phrases.   Diophantine equation, Pell equations.


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DOI: 10.3336/gm.53.1.04


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