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Article . 2015
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Acta Arithmetica
Article . 2015 . Peer-reviewed
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https://dx.doi.org/10.4064/aa1...
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A note on ternary purely exponential diophantine equations

A note on ternary purely exponential Diophantine equations
descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2015 English Publisher:Institute of Mathematics, Polish Academy of SciencesJournal:Acta Arithmetica, volume 171, pages 173-182 (issn: 0065-1036, eissn: 1730-6264, Copyright policy )
Authors: Hu, Yongzhong; Le, Maohua;

doi: 10.4064/aa171-2-4

A note on ternary purely exponential diophantine equations

Abstract

Summary: Let \(a,b,c\) be fixed coprime positive integers with \(\min\{a,b,c\}>1\), and let \(m=\max \{a,b,c\}\). Using the Gel'fond-Baker method, we prove that all positive integer solutions \((x,y,z)\) of the equation \(a^x+b^y=c^z\) satisfy \(\max \{x,y,z\}1\).

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Keywords

ternary purely exponential Diophantine equation, upper bound for solutions, Counting solutions of Diophantine equations, counting solutions, Exponential Diophantine equations

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
6
Top 10%
Top 10%
Average
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