On the Odd Prime Solutions of the Diophantine Equation xy+yx=zz

Yuanyuan Deng; Wenpeng Zhang

doi:10.1155/2014/186416

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Home > Journals > Abstr. Appl. Anal. > Volume 2014 > Article

2014 On the Odd Prime Solutions of the Diophantine Equation

{x}^{y}+{y}^{x}={z}^{z}

Yuanyuan Deng, Wenpeng Zhang

Abstr. Appl. Anal. 2014: 1-4 (2014). DOI: 10.1155/2014/186416

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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.

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Yuanyuan Deng. Wenpeng Zhang. "On the Odd Prime Solutions of the Diophantine Equation ${x}^{y}+{y}^{x}={z}^{z}$ ." Abstr. Appl. Anal. 2014 1 - 4, 2014. https://doi.org/10.1155/2014/186416