Integers representable as differences of linear recurrence sequences

Robert Tichy; Ingrid Vukusic; Daodao Yang; Volker Ziegler

doi:10.1007/s40993-021-00252-2

Integers representable as differences of linear recurrence sequences

Robert Tichy, Ingrid Vukusic, Daodao Yang, Volker Ziegler^*

^*Corresponding author for this work

Institute of Analysis and Number Theory (5010)

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

Abstract

Let {Un}n≥0 and {Vm}m≥0 be two linear recurrence sequences. We establish an asymptotic formula for the number of integers c in the range [- x, x] which can be represented as differences U _n- V _m. In particular, the density of such integers is 0.

Original language	English
Article number	24
Journal	Research in Number Theory
Volume	7
Issue number	2
Early online date	18 Mar 2021
DOIs	https://doi.org/10.1007/s40993-021-00252-2
Publication status	Published - Jun 2021

Keywords

math.NT
Pillai’s problem
Diophantine equations
Recurrence sequence

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1007/s40993-021-00252-2Licence: CC BY 4.0

Cite this

@article{c69890b9f2464518964218cc2d0240ae,

title = "Integers representable as differences of linear recurrence sequences",

abstract = "Let {Un}n≥0 and {Vm}m≥0 be two linear recurrence sequences. We establish an asymptotic formula for the number of integers c in the range [- x, x] which can be represented as differences U n- V m. In particular, the density of such integers is 0. ",

keywords = "math.NT, Pillai{\textquoteright}s problem, Diophantine equations, Recurrence sequence",

author = "Robert Tichy and Ingrid Vukusic and Daodao Yang and Volker Ziegler",

year = "2021",

month = jun,

doi = "10.1007/s40993-021-00252-2",

language = "English",

volume = "7",

journal = "Research in Number Theory",

issn = "2363-9555",

publisher = "Springer",

number = "2",

}

TY - JOUR

T1 - Integers representable as differences of linear recurrence sequences

AU - Tichy, Robert

AU - Vukusic, Ingrid

AU - Yang, Daodao

AU - Ziegler, Volker

PY - 2021/6

Y1 - 2021/6

N2 - Let {Un}n≥0 and {Vm}m≥0 be two linear recurrence sequences. We establish an asymptotic formula for the number of integers c in the range [- x, x] which can be represented as differences U n- V m. In particular, the density of such integers is 0.

AB - Let {Un}n≥0 and {Vm}m≥0 be two linear recurrence sequences. We establish an asymptotic formula for the number of integers c in the range [- x, x] which can be represented as differences U n- V m. In particular, the density of such integers is 0.

KW - math.NT

KW - Pillai’s problem

KW - Diophantine equations

KW - Recurrence sequence

UR - http://www.scopus.com/inward/record.url?scp=85102780477&partnerID=8YFLogxK

U2 - 10.1007/s40993-021-00252-2

DO - 10.1007/s40993-021-00252-2

M3 - Article

SN - 2363-9555

VL - 7

JO - Research in Number Theory

JF - Research in Number Theory

IS - 2

M1 - 24

ER -

Integers representable as differences of linear recurrence sequences

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this