IJPAM: Volume 94, No. 1 (2014)

ON THE DIOPHANTINE EQUATION
$(2^{k}-1)^{x}+(2^{k})^{y}=z^{2}$
WHERE $k$ IS AN EVEN POSITIVE INTEGER

Chantana Simtrakankul
Division of Mathematics
Department of Science
Faculty of Science and Technology
Loei Rajabhat University
Loei, 42000, THAILAND


Abstract. In this paper,we will apply the Catalan's conjecture in oder to give the solution in non-negative integer of the Diophantine equation $(2^{k}-1)^{x}+(2^{k})^{y}=z^{2}$ where $k$ is an even positive integer.

Received: January 16, 2014

AMS Subject Classification: 11D61

Key Words and Phrases: exponential Diophantine equation

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DOI: 10.12732/ijpam.v94i1.7 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: 1
Pages: 65 - 69

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).