On Pell, Pell-Lucas, and balancing numbers

In this paper, we derive some identities on Pell, Pell-Lucas, and balancing numbers and the relationships between them. We also deduce some formulas on the sums, divisibility properties, perfect squares, Pythagorean triples involving these numbers. Moreover, we obtain the set of positive integer sol...

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Detalles Bibliográficos
Autor principal: Karadeniz Gözeri, Gül
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5754423/
https://www.ncbi.nlm.nih.gov/pubmed/29367815
http://dx.doi.org/10.1186/s13660-017-1599-1
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author Karadeniz Gözeri, Gül
author_facet Karadeniz Gözeri, Gül
author_sort Karadeniz Gözeri, Gül
collection PubMed
description In this paper, we derive some identities on Pell, Pell-Lucas, and balancing numbers and the relationships between them. We also deduce some formulas on the sums, divisibility properties, perfect squares, Pythagorean triples involving these numbers. Moreover, we obtain the set of positive integer solutions of some specific Pell equations in terms of the integer sequences mentioned in the text.
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spelling pubmed-57544232018-01-22 On Pell, Pell-Lucas, and balancing numbers Karadeniz Gözeri, Gül J Inequal Appl Research In this paper, we derive some identities on Pell, Pell-Lucas, and balancing numbers and the relationships between them. We also deduce some formulas on the sums, divisibility properties, perfect squares, Pythagorean triples involving these numbers. Moreover, we obtain the set of positive integer solutions of some specific Pell equations in terms of the integer sequences mentioned in the text. Springer International Publishing 2018-01-04 2018 /pmc/articles/PMC5754423/ /pubmed/29367815 http://dx.doi.org/10.1186/s13660-017-1599-1 Text en © The Author(s) 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Karadeniz Gözeri, Gül
On Pell, Pell-Lucas, and balancing numbers
title On Pell, Pell-Lucas, and balancing numbers
title_full On Pell, Pell-Lucas, and balancing numbers
title_fullStr On Pell, Pell-Lucas, and balancing numbers
title_full_unstemmed On Pell, Pell-Lucas, and balancing numbers
title_short On Pell, Pell-Lucas, and balancing numbers
title_sort on pell, pell-lucas, and balancing numbers
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5754423/
https://www.ncbi.nlm.nih.gov/pubmed/29367815
http://dx.doi.org/10.1186/s13660-017-1599-1
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