IJPAM: Volume 94, No. 5 (2014)

ON THE DIOPHANTINE EQUATION $p^x+(p+1)^y=z^2$

Alongkot Suvarnamani
Department of Mathematics
Faculty of Science and Technology
Rajamangala University of Technology Thanyaburi
Thanyaburi, Pathum Thani, 12110, THAILAND


Abstract. In this paper, we found that $(p,x,y,z)=(3,1,0,2)$ is a unique solution of the Diophantine equation $p^x+(p+1)^y=z^2$, where $p$ is an odd prime number and $x$, $y$ and $z$ are non-negative integers.

Received: March 25, 2014

AMS Subject Classification: 11D61

Key Words and Phrases: Diophantine equations, exponential equations

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DOI: 10.12732/ijpam.v94i5.5 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: 2014
Volume: 94
Issue: 5
Pages: 689 - 692


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