The exponential diophantine equation xy + yx = z2 via a generalization of the Ankeny–Artin–Chowla conjecture

DOI10.1142/S1793042118500756zbMath1428.11063OpenAlexW2773342583WikidataQ115522995 ScholiaQ115522995MaRDI QIDQ4643776

Hai Yang, Ruiqin Fu

Publication date: 29 May 2018

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s1793042118500756

zbMATH Keywords

exponential Diophantine equationexceptional numbergeneralized Ankeny-Artin-Chowla conjecture

Mathematics Subject Classification ID

Exponential Diophantine equations (11D61)

Related Items (1)

Some exponential Diophantine equations. II: The equation \(x^2 - dy^2=k^z\) for even \(k\)

Cites Work

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• The exponential Diophantine equation \(x^y + y^x = y^2\) with \(xy\) odd
• Some exponential diophantine equations. I: The equation \(D_1x^2 - D_2y^2 = \lambda k^z\)
• On the Diophantine equation \(y^x-x^y=z^2\)
• The class-number of real quadratic number fields
• Computer verification of the Ankeny--Artin--Chowla Conjecture for all primes less than $100000000000$
• Existence of primitive divisors of Lucas and Lehmer numbers
• On a Pellian equation conjecture
• On the equation \(y^x\pm x^y=z^2\)

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