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The Scientific World Journal
Volume 2014, Article ID 401816, 3 pages
http://dx.doi.org/10.1155/2014/401816
Research Article

The Exponential Diophantine Equation

1Luoyang Institute of Science and Technology, Luoyang, Henan 471023, China
2School of Mathematics, Northwest University, Xi'an, Shaanxi 710127, China

Received 1 April 2014; Accepted 6 May 2014; Published 18 May 2014

Academic Editor: Abdelghani Bellouquid

Copyright © 2014 Yahui Yu and Xiaoxue Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let and be fixed coprime odd positive integers with . In this paper, a classification of all positive integer solutions of the equation is given. Further, by an elementary approach, we prove that if , then the equation has only the positive integer solution , except for and , where is a positive integer with .