Glasnik Matematicki, Vol. 51, No. 1 (2016), 17-22.

ON TWO DIOPHANTINE EQUATIONS OF RAMANUJAN-NAGELL TYPE

Zhongfeng Zhang and Alain Togbé

Zhaoqing University, China and Purdue University North Central, USA

Department of Mathematics, Purdue University North Central, 1401 S. U.S. 421 Westville IN 46391, USA
e-mail: atogbe@pnc.edu

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.

2010 Mathematics Subject Classification.   11D41.

Key words and phrases.   Diophantine equation.

Full text (PDF) (free access)

DOI: 10.3336/gm.51.1.02

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