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Glasnik matematički, Vol. 56 No. 2, 2021.

Original scientific paper

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

On the Ramanujan-Nagell type Diophantine equation \(Dx^2+k^n=B\)

Zhongfeng Zhang orcid id orcid.org/0000-0002-1711-427X ; School of Mathematics and Statistics, Zhaoqing University, Zhaoqing 526061, China
Alain Togbé orcid id orcid.org/0000-0002-5882-936X ; Department of Mathematics and Statistics, Purdue University Northwest, 1401 S. U.S. 421 Westville, IN 46391, USA

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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.

Keywords

Diophantine equation, Pell equations.

Hrčak ID:

267556

URI

https://hrcak.srce.hr/267556

Publication date:

23.12.2021.

Visits: 424 *

Publication date: 31 December 2021

Volume: Vol 56

Issue: Svezak 2

Pages: 263-270

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

Article Information (continued)

Categories:

Subject: Izvorni znanstveni članak

Keywords:

Keyword: Diophantine equation, Pell equations.

On the Ramanujan-Nagell type Diophantine equation \(Dx^2+k^n=B\)

Zhongfeng Zhang[1]

Email: bee2357@163.com

Alain Togbé[2]

Email: atogbe@pnw.edu

 

[1] School of Mathematics and Statistics, Zhaoqing University, Zhaoqing 526061, China

[2] Department of Mathematics and Statistics, 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 \(Dx^2+k^n=B\) has at most three nonnegative integer solutions \((x, n)\) for \(k\) a prime and \(B, D\) positive integers.

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