On a variant of Pillai's problem II

Kwok Chi Chim; István Pink; Volker Ziegler

doi:10.1016/j.jnt.2017.07.016

On a variant of Pillai's problem II

Kwok Chi Chim, István Pink, Volker Ziegler

Institute of Analysis and Number Theory (5010)

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we show that there are only finitely many $c$ such that the equation $U_n - V_m = c$ has at least two distinct solutions $(n,m)$, where $\{U_n\}_{n\geq 0}$ and $\{V_m\}_{m\geq 0}$ are given linear recurrence sequences.

Original language	English
Pages (from-to)	269-290
Journal	Journal of Number Theory
Volume	183
DOIs	https://doi.org/10.1016/j.jnt.2017.07.016
Publication status	Published - 2018

Keywords

math.NT
Diophantine equations
Pillai's problem
Recurrence sequence

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1016/j.jnt.2017.07.016

Cite this

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title = "On a variant of Pillai's problem II",

abstract = "In this paper, we show that there are only finitely many $c$ such that the equation $U_n - V_m = c$ has at least two distinct solutions $(n,m)$, where $\{U_n\}_{n\geq 0}$ and $\{V_m\}_{m\geq 0}$ are given linear recurrence sequences.",

keywords = "math.NT, Diophantine equations, Pillai's problem, Recurrence sequence",

author = "Chim, {Kwok Chi} and Istv{\'a}n Pink and Volker Ziegler",

year = "2018",

doi = "10.1016/j.jnt.2017.07.016",

language = "English",

volume = "183",

pages = "269--290",

journal = "Journal of Number Theory",

publisher = "Academic Press",

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AU - Pink, István

AU - Ziegler, Volker

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AB - In this paper, we show that there are only finitely many $c$ such that the equation $U_n - V_m = c$ has at least two distinct solutions $(n,m)$, where $\{U_n\}_{n\geq 0}$ and $\{V_m\}_{m\geq 0}$ are given linear recurrence sequences.

KW - math.NT

KW - Diophantine equations

KW - Pillai's problem

KW - Recurrence sequence

U2 - 10.1016/j.jnt.2017.07.016

DO - 10.1016/j.jnt.2017.07.016

M3 - Article

VL - 183

SP - 269

EP - 290

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -