IJPAM: Volume 103, No. 2 (2015)

SOLUTION OF THE DIOPHANTINE EQUATION
$(2^k-1)^x+(2^k)^y=z^2$

Alongkot Suvarnamani$^1$, Tawan Ampawa$^2$
$^{1,2}$Department of Mathematics
Faculty of Science and Technology
Rajamangala University of Technology Thanyaburi
Thanyaburi, Pathum Thani, 12110, THAILAND


Abstract. In this paper, we will apply the Catalan's conjecture to find the solution of the Diophantine equation $(2^k-1)^x+(2^k)^y=z^2$ where $k$ is an odd integer at least 3.

Received: September 17, 2014

AMS Subject Classification: 11D61

Key Words and Phrases: Diophantine equations, exponential equations

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DOI: 10.12732/ijpam.v103i2.2 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: 2015
Volume: 103
Issue: 2
Pages: 159 - 162


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