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^*

^*Korrespondierende/r Autor/-in für diese Arbeit

Institut für Analysis und Zahlentheorie (5010)

Publikation: Beitrag in einer Fachzeitschrift › Artikel › Begutachtung

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.

Originalsprache	englisch
Aufsatznummer	24
Fachzeitschrift	Research in Number Theory
Jahrgang	7
Ausgabenummer	2
Frühes Online-Datum	18 März 2021
DOIs	https://doi.org/10.1007/s40993-021-00252-2
Publikationsstatus	Veröffentlicht - Juni 2021

ASJC Scopus subject areas

Algebra und Zahlentheorie

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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

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Integers representable as differences of linear recurrence sequences

Abstract

ASJC Scopus subject areas

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