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The Scientific World Journal
Volume 2015, Article ID 306590, 3 pages
Research Article

The Diophantine Equation

1College of Mathematics and Statistics, Yulin University, Yulin, Shaanxi 719000, China
2School of Mathematics, Northwest University, Xi’an, Shaanxi 710127, China

Received 7 July 2014; Accepted 14 December 2014

Academic Editor: Abdelghani Bellouquid

Copyright © 2015 Lan Qi 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.


Let be a fixed odd prime. Using certain results of exponential Diophantine equations, we prove that (i) if , then the equation has no positive integer solutions ; (ii) if , then the equation has only the solutions , where is an odd prime with ; (iii) if and , then the equation has at most two positive integer solutions .