Complete solution of the Diophantine equation $x^y+y^x=z^z$

DOI10.21136/CMJ.2018.0395-17OpenAlexW2886588644MaRDI QIDQ5227118

Mihai Cipu

Publication date: 5 August 2019

Published in: Czechoslovak Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.21136/cmj.2018.0395-17

zbMATH Keywords

sievingexponential Diophantine equationmodular computations

Mathematics Subject Classification ID

Exponential Diophantine equations (11D61) Power residues, reciprocity (11A15)

Uses Software

• PARI/GP

Cites Work

• On the odd prime solutions of the Diophantine equation \(x^y + y^x = z^z\)
• Computer verification of the Ankeny--Artin--Chowla Conjecture for all primes less than $100000000000$
• Linear forms in p-adic logarithms and the Diophantine equation formula here
• On the exponential diophantine equation $x^y+y^x=z^z$
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