Integers representable as differences of linear recurrence sequences

Let [Formula: see text] and [Formula: see text] be two linear recurrence sequences. We establish an asymptotic formula for the number of integers c in the range [Formula: see text] which can be represented as differences [Formula: see text] . In particular, the density of such integers is 0.

Detalles Bibliográficos
Autores principales: Tichy, Robert, Vukusic, Ingrid, Yang, Daodao, Ziegler, Volker
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2021
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8550782/
https://www.ncbi.nlm.nih.gov/pubmed/34723093
http://dx.doi.org/10.1007/s40993-021-00252-2
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author Tichy, Robert
Vukusic, Ingrid
Yang, Daodao
Ziegler, Volker
author_facet Tichy, Robert
Vukusic, Ingrid
Yang, Daodao
Ziegler, Volker
author_sort Tichy, Robert
collection PubMed
description Let [Formula: see text] and [Formula: see text] be two linear recurrence sequences. We establish an asymptotic formula for the number of integers c in the range [Formula: see text] which can be represented as differences [Formula: see text] . In particular, the density of such integers is 0.
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spelling pubmed-85507822021-10-29 Integers representable as differences of linear recurrence sequences Tichy, Robert Vukusic, Ingrid Yang, Daodao Ziegler, Volker Res Number Theory Research Let [Formula: see text] and [Formula: see text] be two linear recurrence sequences. We establish an asymptotic formula for the number of integers c in the range [Formula: see text] which can be represented as differences [Formula: see text] . In particular, the density of such integers is 0. Springer International Publishing 2021-03-18 2021 /pmc/articles/PMC8550782/ /pubmed/34723093 http://dx.doi.org/10.1007/s40993-021-00252-2 Text en © The Author(s) 2021 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Research
Tichy, Robert
Vukusic, Ingrid
Yang, Daodao
Ziegler, Volker
Integers representable as differences of linear recurrence sequences
title Integers representable as differences of linear recurrence sequences
title_full Integers representable as differences of linear recurrence sequences
title_fullStr Integers representable as differences of linear recurrence sequences
title_full_unstemmed Integers representable as differences of linear recurrence sequences
title_short Integers representable as differences of linear recurrence sequences
title_sort integers representable as differences of linear recurrence sequences
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8550782/
https://www.ncbi.nlm.nih.gov/pubmed/34723093
http://dx.doi.org/10.1007/s40993-021-00252-2
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AT yangdaodao integersrepresentableasdifferencesoflinearrecurrencesequences
AT zieglervolker integersrepresentableasdifferencesoflinearrecurrencesequences

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