On the x-coordinates of Pell equations that are sums of two Padovan numbers

Let [Formula: see text] be the sequence of Padovan numbers defined by [Formula: see text] , [Formula: see text] , and [Formula: see text] for all [Formula: see text] . In this paper, we find all positive square-free integers d such that the Pell equations [Formula: see text] with [Formula: see text]...

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Autor principal: Ddamulira, Mahadi
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2021
Materias:
Original Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7900383/
https://www.ncbi.nlm.nih.gov/pubmed/33678911
http://dx.doi.org/10.1007/s40590-021-00312-8
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author Ddamulira, Mahadi
author_facet Ddamulira, Mahadi
author_sort Ddamulira, Mahadi
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description Let [Formula: see text] be the sequence of Padovan numbers defined by [Formula: see text] , [Formula: see text] , and [Formula: see text] for all [Formula: see text] . In this paper, we find all positive square-free integers d such that the Pell equations [Formula: see text] with [Formula: see text] , have at least two positive integer solutions (x, y) and [Formula: see text] such that both x and [Formula: see text] are sums of two Padovan numbers.
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spelling pubmed-79003832021-03-05 On the x-coordinates of Pell equations that are sums of two Padovan numbers Ddamulira, Mahadi Bol Soc Mat Mex Original Article Let [Formula: see text] be the sequence of Padovan numbers defined by [Formula: see text] , [Formula: see text] , and [Formula: see text] for all [Formula: see text] . In this paper, we find all positive square-free integers d such that the Pell equations [Formula: see text] with [Formula: see text] , have at least two positive integer solutions (x, y) and [Formula: see text] such that both x and [Formula: see text] are sums of two Padovan numbers. Springer International Publishing 2021-02-23 2021 /pmc/articles/PMC7900383/ /pubmed/33678911 http://dx.doi.org/10.1007/s40590-021-00312-8 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 Original Article
Ddamulira, Mahadi
On the x-coordinates of Pell equations that are sums of two Padovan numbers
title On the x-coordinates of Pell equations that are sums of two Padovan numbers
title_full On the x-coordinates of Pell equations that are sums of two Padovan numbers
title_fullStr On the x-coordinates of Pell equations that are sums of two Padovan numbers
title_full_unstemmed On the x-coordinates of Pell equations that are sums of two Padovan numbers
title_short On the x-coordinates of Pell equations that are sums of two Padovan numbers
title_sort on the x-coordinates of pell equations that are sums of two padovan numbers
topic Original Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7900383/
https://www.ncbi.nlm.nih.gov/pubmed/33678911
http://dx.doi.org/10.1007/s40590-021-00312-8
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