Glasnik matematički, Vol. 51 No. 1, 2016.
Original scientific paper
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
Abstract
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.
Keywords
Hrčak ID:
160100
URI
Publication date:
15.6.2016.
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