Glasnik matematički, Vol. 53 No. 1, 2018.
Original scientific paper
https://doi.org/10.3336/gm.53.1.04
On the Ramanujan-Nagell type Diophantine equation \(x^2+Ak^n=B\)
Zhongfeng Zhang
; School of Mathematics and Statistics, Zhaoqing University, Zhaoqing 526061, China
Alain Togbé
orcid.org/0000-0002-5882-936X
; Department of Mathematics, Statistics and Computer Science, Purdue University Northwest, 1401 S. U.S. 421 Westville, IN 46391, USA
Abstract
In this paper, we prove that the Ramanujan-Nagell type Diophantine equation \(x^2+Ak^n=B\) 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].
Keywords
Diophantine equation; Pell equations
Hrčak ID:
201810
URI
Publication date:
20.6.2018.
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