Abstract and Applied Analysis

On the Odd Prime Solutions of the Diophantine Equation x y + y x = z z

Yuanyuan Deng and Wenpeng Zhang

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Abstract

Using the elementary method and some properties of the least solution of Pell’s equation, we prove that the equation x y + y x = z z has no positive integer solutions ( x , y , z ) with x and y being odd primes.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 186416, 4 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412277108

Digital Object Identifier
doi:10.1155/2014/186416

Mathematical Reviews number (MathSciNet)
MR3240527

Zentralblatt MATH identifier
07021895

Citation

Deng, Yuanyuan; Zhang, Wenpeng. On the Odd Prime Solutions of the Diophantine Equation ${x}^{y}+{y}^{x}={z}^{z}$. Abstr. Appl. Anal. 2014 (2014), Article ID 186416, 4 pages. doi:10.1155/2014/186416. https://projecteuclid.org/euclid.aaa/1412277108


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