The generalized Pillai equation \(\pm ra^x\pm sb^y=c\)

DOI10.1016/j.jnt.2010.11.004zbMath1244.11030OpenAlexW2315831193MaRDI QIDQ531838

Robert Styer, Reese Scott

Publication date: 20 April 2011

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2010.11.004

zbMATH Keywords

exponential Diophantine equationsPillai's equation

Mathematics Subject Classification ID

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

Related Items (2)

The number of solutions to the generalized Pillai equation \(\pm ra^{x} \pm sb^{y}=c\). ⋮ Number of solutions to \(ka^x+lb^y=c^z\)

Cites Work

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• On the equations \(p^x - b^y = c\) and \(a^x + b^y = c^z\)
• On Pillai's Diophantine equation
• On the generalized Pillai equation \(\pm a^{x}\pm b^{y}=c\)
• A note on the diophantine equation \(ax^ m - by^ n = k\)
• On \(p^x-q^y=c\) and related three term exponential Diophantine equations with prime bases.
• On the number of solutions of Goormaghtigh equation for given \(x\) and \(y\)
• Rational approximation to algebraic numbers of small height: the Diophantine equation |axn - byn|= 1
• On Some Exponential Equations of S. S. Pillai
• An explicit lower bound for a homogeneous rational linear form in the logarithms of algebraic numbers. II
• Primes at a Glance
• Small Two-Variable Exponential Diophantine Equations

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