Izvorni znanstveni članak

https://doi.org/10.3336/gm.51.1.02

On two Diophantine equations of Ramanujan-Nagell type

Zhongfeng Zhang ; Zhaoqing University, China and Purdue University North Central, USA
Alain Togbé orcid.org/0000-0002-5882-936X ; Department of Mathematics, Purdue University North Central, 1401 S. U.S. 421 Westville IN 46391, USA

Sažetak

In this paper, we prove two conjectures of Ulas ([21]) on two Diophantine equations of Ramanujan-Nagell type. In fact, we show that the following equations


x2+(2m+1+1)2n=24(m+1)+23(m+1)+22m+2m+1+1,
x2+(22m+6-1)2n/3 = (49 · 42m+5-11· 4m+3+1)/9

have exactly four solutions.

Ključne riječi

Diophantine equation

Hrčak ID:

160100

URI

https://hrcak.srce.hr/160100

Datum izdavanja:

15.6.2016.

Posjeta: 1.819 *