ON THE NUMBER OF SOLUTIONS OF THE DIOPHANTINE EQUATIONaxm−byn=c

DOI10.1017/S0004972709001002zbMath1251.11019OpenAlexW2160769883MaRDI QIDQ3552476

Bo He, Alain S. Togbé

Publication date: 22 April 2010

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0004972709001002

zbMATH Keywords

linear forms in logarithmsBaker's methodexponential diophantine equationsCatalan-Pillai equation

Mathematics Subject Classification ID

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

Related Items (3)

On the existence of numbers with matching continued fraction and base \(b\) expansions ⋮ The number of solutions to the generalized Pillai equation \(\pm ra^{x} \pm sb^{y}=c\). ⋮ Number of solutions to \(ka^x+lb^y=c^z\)

Uses Software

• PARI/GP

Cites Work

• Unnamed Item
• A note on the diophantine equation \(ax^ m - by^ n = k\)
• On the Diophantine equation \(\frac{x^m-1}{x-1}=\frac{y^n-1}{y-1}\).
• On the number of solutions of Goormaghtigh equation for given \(x\) and \(y\)
• 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
• The equation 2^{𝑥}-3^{𝑦}=𝑑
• On the Equation a x - b y = 1

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