IJPAM: Volume 88, No. 2 (2013)

ON THE DIOPHANTINE EQUATION
$p^x+(p+1)^y=z^2$ WHERE $p$ IS A MERSENNE PRIME

Somchit Chotchaisthit
Department of Mathematics
Faculty of Science
Khon Kaen University
Khon Kaen, 40002, THAILAND


Abstract. In this paper we show that $(p,x,y,z)=(7,0,1,3)$ and $(p,x,y,z)=(3,2,2,5)$ are the only solutions to the Diophantine equation $p^x+(p+1)^y=z^2$, where $x,y,z$ are non-negative integers and p is a Mersenne prime.

Received: May 22, 2013

AMS Subject Classification: 11D61

Key Words and Phrases: exponential Diophantine equation

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DOI: 10.12732/ijpam.v88i2.2 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 88
Issue: 2