A purely exponential Diophantine equation in three unknowns

DOI10.1007/s10998-021-00405-xOpenAlexW3182653121WikidataQ115603580 ScholiaQ115603580MaRDI QIDQ2151162

Takafumi Miyazaki, Nobuhiro Terai, Masaki Sudo

Publication date: 30 June 2022

Published in: Periodica Mathematica Hungarica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10998-021-00405-x

zbMATH Keywords

linear forms in logarithmsBaker's method\(S\)-unit equationpurely exponential equationsimultaneous non-Archimedean valuations

Mathematics Subject Classification ID

Exponential Diophantine equations (11D61) Linear forms in logarithms; Baker's method (11J86)

Related Items (1)

A note on the ternary purely exponential Diophantine equation \(f^x + (f + g)^y = g^z\)

Cites Work

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• On Jeśmanowicz' conjecture concerning primitive Pythagorean triples
• On the equations \(p^x - b^y = c\) and \(a^x + b^y = c^z\)
• The Magma algebra system. I: The user language
• An upper bound for the number of solutions of ternary purely exponential Diophantine equations
• Upper bounds for solutions of an exponential Diophantine equation
• On the Diophantine equation \(a^x+b^y=(a+2)^z\)
• A Hasse-type principle for exponential Diophantine equations and its applications
• On the system of Diophantine equations a²+b²=(m²+1)^rand a^x+b^y=(m²+1)^z
• Unit Equations in Diophantine Number Theory
• Number of solutions to $a^x + b^y = c^z$
• On a conjecture on exponential Diophantine equations
• Contributions to some conjectures on a ternary exponential Diophantine equation
• A Survey on the Ternary Purely Exponential Diophantine Equation $a^x + b^y = c^z$
• A study on the exponential Diophantine equation $a^x+(a+b)^y=b^z$
• An upper bound for the number of solutions of ternary purely exponential Diophantine equations II

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