Izvorni znanstveni članak

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

Sažetak

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].

Ključne riječi

Diophantine equation; Pell equations

Hrčak ID:

201810

URI

https://hrcak.srce.hr/201810

Datum izdavanja:

20.6.2018.

Posjeta: 1.265 *