Handling a large bound for a problem on the generalized Pillai equation \(\pm r a^{x} \pm sb^{y}=c\)
type: Item
instance of: scholarly article
zbMATH Open document ID: 1308.11040
author: Reese Scott
author: Robert Styer
publication date: 2014-10-23T00:00:00Z
full work available at URL: https://arxiv.org/abs/1112.4547
full work available at URL: o49.Abstract.html
Mathematics Subject Classification ID: 11D61
zbMATH DE Number: 6360721
zbMATH Keywords: exponential equation
zbMATH Keywords: Pillai equation
zbMATH Keywords: number of solutions
MaRDI profile type: Publication
arXiv ID: 1112.4547
arXiv classification: math.NT
Recommended article: On the generalized Pillai equation \(\pm a^{x}\pm b^{y}=c\)
Recommended article: Large solutions to the \(p\)-Laplacian for large \(p\)
Recommended article: A Hilbert boundary value problem for generalised Cauchy-Riemann equations
Recommended article: Q3752655
Recommended article: The number of solutions to the generalized Pillai equation \(\pm ra^{x} \pm sb^{y}=c\).
Recommended article: On a boundedness condition for solutions of a generalized Liénard equation
Recommended article: On behavior of solution of boundary value problem for generalized Cauchy-Riemann equation
Recommended article: Remark on solvability of \(p\)-Laplacian equations in large dimension
Recommended article: Q3331487
Recommended article: Q3151352
title: Handling a large bound for a problem on the generalized Pillai equation \(\pm r a^{x} \pm sb^{y}=c\)
published in: Integers
review text: Consider the equation \((-1)^ura^x+(-1)^vsb^y=c\) in nonnegative integers \(x,y\) and \(u,v\in\{0,1\}\), where \(a,b,c,r,s\) are given positive integers with \(a>1\), \(b>1\). Write \(N\) for the number of solutions in \((x,y,u,v)\).NEWLINENEWLINEIn a previous paper the authors proved that there are essentially nine distinct tuples \((a,b,c,r,s)\) allowing \(N\geq 4\) solutions, except possibly the cases where \(a,b,r,s,x,y\) are all smaller than \(2\cdot 10^{15}\). In the present paper the authors prove that no new solutions arise for these small values of the parameters. The present paper is more general than the previous work in that now \(x\) and \(y\) can also be zero, and \((u,v)\) may differ from \((0,1)\).
reviewed by: Lajos Hajdu
description: scientific article; zbMATH DE number 6360721