On the odd prime solutions of the Diophantine equation \(x^y + y^x = z^z\)
type: Item
instance of: scholarly article
title: On the odd prime solutions of the Diophantine equation \(x^y + y^x = z^z\)
zbMATH Open document ID: 1470.11053
DOI: 10.1155/2014/186416
author: Yuanyuan Deng
author: Wenpeng Zhang
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 11D61
zbMATH DE Number: 7021895
Wikidata QID: Q59035875
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/186416
OpenAlex ID: W1594774501
cites work: On the equation \(y^x\pm x^y=z^2\)
cites work: On the Diophantine equation \(y^x-x^y=z^2\)
cites work: Q3014181
cites work: On the Diophantine equation \(ax^{y} + by^{z} + cz^{x} = 0\)
cites work: Q5166110
cites work: Q3884165
cites work: Computer verification of the Ankeny-Artin-Chowla Conjecture for all primes less than \(100 000 000 000\)
cites work: Q3982418
description: scientific article; zbMATH DE number 7021895