On the exponential Diophantine equation related to powers of two consecutive terms of Lucas sequences

Let [Formula: see text] be an integer and [Formula: see text] be the Lucas sequence given by [Formula: see text] , [Formula: see text] and [Formula: see text] , for all [Formula: see text] . In this paper, we show that there are no positive integers [Formula: see text] such that [Formula: see text]...

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Detalles Bibliográficos
Autores principales: Ddamulira, Mahadi, Luca, Florian
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer US 2020
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8550777/
https://www.ncbi.nlm.nih.gov/pubmed/34720672
http://dx.doi.org/10.1007/s11139-020-00278-7
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author Ddamulira, Mahadi
Luca, Florian
author_facet Ddamulira, Mahadi
Luca, Florian
author_sort Ddamulira, Mahadi
collection PubMed
description Let [Formula: see text] be an integer and [Formula: see text] be the Lucas sequence given by [Formula: see text] , [Formula: see text] and [Formula: see text] , for all [Formula: see text] . In this paper, we show that there are no positive integers [Formula: see text] such that [Formula: see text] is a member of [Formula: see text] .
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spelling pubmed-85507772021-10-29 On the exponential Diophantine equation related to powers of two consecutive terms of Lucas sequences Ddamulira, Mahadi Luca, Florian Ramanujan J Article Let [Formula: see text] be an integer and [Formula: see text] be the Lucas sequence given by [Formula: see text] , [Formula: see text] and [Formula: see text] , for all [Formula: see text] . In this paper, we show that there are no positive integers [Formula: see text] such that [Formula: see text] is a member of [Formula: see text] . Springer US 2020-07-23 2021 /pmc/articles/PMC8550777/ /pubmed/34720672 http://dx.doi.org/10.1007/s11139-020-00278-7 Text en © The Author(s) 2020 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 Article
Ddamulira, Mahadi
Luca, Florian
On the exponential Diophantine equation related to powers of two consecutive terms of Lucas sequences
title On the exponential Diophantine equation related to powers of two consecutive terms of Lucas sequences
title_full On the exponential Diophantine equation related to powers of two consecutive terms of Lucas sequences
title_fullStr On the exponential Diophantine equation related to powers of two consecutive terms of Lucas sequences
title_full_unstemmed On the exponential Diophantine equation related to powers of two consecutive terms of Lucas sequences
title_short On the exponential Diophantine equation related to powers of two consecutive terms of Lucas sequences
title_sort on the exponential diophantine equation related to powers of two consecutive terms of lucas sequences
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8550777/
https://www.ncbi.nlm.nih.gov/pubmed/34720672
http://dx.doi.org/10.1007/s11139-020-00278-7
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