9-Modularity and GCD Properties of Generalized Fibonacci Numbers

ABSTRACT: We study 9-modularity properties of generalized Fibonacci numbers that give rise to well-known quasigroups. In this paper we also study GCD and divisibility properties of generalized Fibonacci numbers. This study includes necessary and su cient conditions to determine whether the GCD of tw...

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Autores:
Floréz, Rigoberto
Higuita Díaz, Robinson Alexander
Junes, Leandro
Tipo de recurso:
Article of journal
Fecha de publicación:
2014
Institución:
Universidad de Antioquia
Repositorio:
Repositorio UdeA
Idioma:
eng
OAI Identifier:
oai:bibliotecadigital.udea.edu.co:10495/20362
Acceso en línea:
http://hdl.handle.net/10495/20362
http://math.colgate.edu/~integers/o55/o55.pdf
Palabra clave:
Números de Fibonacci
Secuencias Fibonacci
Rights
openAccess
License
http://creativecommons.org/licenses/by/2.5/co/
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network_name_str Repositorio UdeA
repository_id_str
dc.title.spa.fl_str_mv 9-Modularity and GCD Properties of Generalized Fibonacci Numbers
title 9-Modularity and GCD Properties of Generalized Fibonacci Numbers
spellingShingle 9-Modularity and GCD Properties of Generalized Fibonacci Numbers
Números de Fibonacci
Secuencias Fibonacci
title_short 9-Modularity and GCD Properties of Generalized Fibonacci Numbers
title_full 9-Modularity and GCD Properties of Generalized Fibonacci Numbers
title_fullStr 9-Modularity and GCD Properties of Generalized Fibonacci Numbers
title_full_unstemmed 9-Modularity and GCD Properties of Generalized Fibonacci Numbers
title_sort 9-Modularity and GCD Properties of Generalized Fibonacci Numbers
dc.creator.fl_str_mv Floréz, Rigoberto
Higuita Díaz, Robinson Alexander
Junes, Leandro
dc.contributor.author.none.fl_str_mv Floréz, Rigoberto
Higuita Díaz, Robinson Alexander
Junes, Leandro
dc.subject.proposal.spa.fl_str_mv Números de Fibonacci
Secuencias Fibonacci
topic Números de Fibonacci
Secuencias Fibonacci
description ABSTRACT: We study 9-modularity properties of generalized Fibonacci numbers that give rise to well-known quasigroups. In this paper we also study GCD and divisibility properties of generalized Fibonacci numbers. This study includes necessary and su cient conditions to determine whether the GCD of two generalized Fibonacci numbers is a regular Fibonacci number.
publishDate 2014
dc.date.issued.none.fl_str_mv 2014
dc.date.accessioned.none.fl_str_mv 2021-06-25T01:02:11Z
dc.date.available.none.fl_str_mv 2021-06-25T01:02:11Z
dc.type.spa.fl_str_mv info:eu-repo/semantics/article
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dc.type.local.spa.fl_str_mv Artículo de revista
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dc.identifier.uri.none.fl_str_mv http://hdl.handle.net/10495/20362
dc.identifier.eissn.none.fl_str_mv 1553-1732
dc.identifier.url.spa.fl_str_mv http://math.colgate.edu/~integers/o55/o55.pdf
url http://hdl.handle.net/10495/20362
http://math.colgate.edu/~integers/o55/o55.pdf
identifier_str_mv 1553-1732
dc.language.iso.spa.fl_str_mv eng
language eng
dc.relation.ispartofjournalabbrev.spa.fl_str_mv Integers
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dc.format.extent.spa.fl_str_mv 14
dc.format.mimetype.spa.fl_str_mv application/pdf
dc.publisher.spa.fl_str_mv Colgate University, Charles University, DIMATIA
dc.publisher.group.spa.fl_str_mv Análisis Numérico y Financiero: Matemáticas aplicadas para la industria
dc.publisher.place.spa.fl_str_mv Estados Unidos
institution Universidad de Antioquia
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spelling Floréz, RigobertoHiguita Díaz, Robinson AlexanderJunes, Leandro2021-06-25T01:02:11Z2021-06-25T01:02:11Z2014http://hdl.handle.net/10495/203621553-1732http://math.colgate.edu/~integers/o55/o55.pdfABSTRACT: We study 9-modularity properties of generalized Fibonacci numbers that give rise to well-known quasigroups. In this paper we also study GCD and divisibility properties of generalized Fibonacci numbers. This study includes necessary and su cient conditions to determine whether the GCD of two generalized Fibonacci numbers is a regular Fibonacci number.COL010637114application/pdfengColgate University, Charles University, DIMATIAAnálisis Numérico y Financiero: Matemáticas aplicadas para la industriaEstados Unidosinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/redcol/resource_type/CJournalArticleArtículo de revistahttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/2.5/co/http://purl.org/coar/access_right/c_abf2https://creativecommons.org/licenses/by/4.0/9-Modularity and GCD Properties of Generalized Fibonacci NumbersNúmeros de FibonacciSecuencias FibonacciIntegersIntegers114141ORIGINALHiguitaRobinson_2014_GeneralizedFibonacciNumbers.pdfHiguitaRobinson_2014_GeneralizedFibonacciNumbers.pdfArtículo de revistaapplication/pdf418889http://bibliotecadigital.udea.edu.co/bitstream/10495/20362/1/HiguitaRobinson_2014_GeneralizedFibonacciNumbers.pdf041381c79c435e451b59ccbc9cd1f0b9MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8927http://bibliotecadigital.udea.edu.co/bitstream/10495/20362/2/license_rdf1646d1f6b96dbbbc38035efc9239ac9cMD52LICENSElicense.txtlicense.txttext/plain; charset=utf-81748http://bibliotecadigital.udea.edu.co/bitstream/10495/20362/3/license.txt8a4605be74aa9ea9d79846c1fba20a33MD5310495/20362oai:bibliotecadigital.udea.edu.co:10495/203622021-06-24 20:02:11.762Repositorio Institucional Universidad de Antioquiaandres.perez@udea.edu.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