IJPAM: Volume 103, No. 2 (2015)

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

Mongkol Tatong$^1$, Alongkot Suvarnamani$^2$
$^{1,2}$Department of Mathematics
Faculty of Science and Technology
Rajamangala University of Technology Thanyaburi (RMUTT)
Thanyaburi, Pathum Thani, 12110, THAILAND


Abstract. In this paper, we found that the Diophantine equation $(p+1)^{2x}+q^y=z^2$ has no non-negative integer solution where $p$ is a Mersenne prime number which $q-p=2$ and $x$, $y$ and $z$ are non-negative integers.

Received: August 21, 2014

AMS Subject Classification: 11D61

Key Words and Phrases: diophantine equations, exponential equations

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DOI: 10.12732/ijpam.v103i2.1 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: 2015
Volume: 103
Issue: 2
Pages: 155 - 158


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