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

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

Cite this

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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. ",

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

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month = jun,

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AU - Tichy, Robert

AU - Vukusic, Ingrid

AU - Yang, Daodao

AU - Ziegler, Volker

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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

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U2 - 10.1007/s40993-021-00252-2

DO - 10.1007/s40993-021-00252-2

M3 - Article

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JO - Research in Number Theory

JF - Research in Number Theory

SN - 2363-9555

IS - 2

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ER -

Integers representable as differences of linear recurrence sequences

Abstract

Keywords

ASJC Scopus subject areas

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