On the generalized Pillai equation \(\pm a^{x}\pm b^{y}=c\)

DOI10.1016/j.jnt.2005.09.001zbMath1146.11020arXiv1102.4834OpenAlexW2047351779WikidataQ56226409 ScholiaQ56226409MaRDI QIDQ852536

Robert Styer, Reese Scott

Publication date: 15 November 2006

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

Full work available at URL: https://arxiv.org/abs/1102.4834

zbMATH Keywords

exponential Diophantine equationsPillai equation

Mathematics Subject Classification ID

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

Related Items (5)

A note on the number of solutions of the Pillai type equation \(| a^x - b^y | = k\) ⋮ The number of solutions to the generalized Pillai equation \(\pm ra^{x} \pm sb^{y}=c\). ⋮ Multiplicative dependence of the translations of algebraic numbers ⋮ Number of solutions to \(ka^x+lb^y=c^z\) ⋮ The generalized Pillai equation \(\pm ra^x\pm sb^y=c\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Solving exponential diophantine equations using lattice basis reduction algorithms
• On the equations \(p^x - b^y = c\) and \(a^x + b^y = c^z\)
• Sur une classe d'équations exponentielles
• The diophantine equation \(x^ 2=4q^{a/2}+4q+1\), with an application to coding theory
• Exponential diophantine equations with four terms
• On \(p^x-q^y=c\) and related three term exponential Diophantine equations with prime bases.
• Applications of the hypergeometric method to the generalized Ramanujan-Nagell equation
• The equations \(2^N\pm 2^M\pm 2^L=z^2\)
• Pillai's conjecture revisited.
• A class number free criterion for Catalan's conjecture.
• On Some Exponential Equations of S. S. Pillai
• New Solutions of a p - 1 ≡1 (mod p 2 )
• Diophantine equations related to finite groups
• On the generalized Ramanujan-Nagell equation I
• A corollary to a theorem of Laurent-Mignotte-Nesterenko
• Catalan’s Conjecture: Another old Diophantine problem solved
• A conjecture concerning the exponential diophantine equation a^x+b^y=c^z
• The Diophantine Equation x 2 = 4q n + 4q m + 1
• Small Two-Variable Exponential Diophantine Equations
• On the Equation a x - b y = 1
• On the Equation a x - b y = 1
• Exponential diophantine equations

This page was built for publication: On the generalized Pillai equation \(\pm a^{x}\pm b^{y}=c\)