Glasnik Matematicki, Vol. 53, No. 2 (2018), 221-228.

ON THE RAMANUJAN-NAGELL TYPE DIOPHANTINE EQUATION x2+Akn=B, II

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
e-mail: atogbe@pnw.edu

Abstract.   Let A, B be positive integers and q a prime. In this paper, we prove that the Ramanujan-Nagell type Diophantine equation x2+Aqn=B has at most four nonnegative integer solutions (x, n) for q2∤ B and B≥ C where C is some constant depending of A. We also prove that the equation x2+3×2n=B has at most four nonnegative integer solutions (x, n). Therefore, we partially confirm a conjecture of Ulas ([4]).

2010 Mathematics Subject Classification.   11D41

Key words and phrases.   Diophantine equations

Full text (PDF) (free access)

DOI: 10.3336/gm.53.2.01

References:

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