Powers of two in generalized fibonacci sequences

The $k-$generalized Fibonacci sequence $\big(F_{n}^{(k)}\big)_{n}$ resembles the Fibonacci sequence in that it starts with $0,\ldots,0,1$ ($k$ terms) and each term afterwards is the sum of the $k$ preceding terms. In this paper, we are interested in finding powers of two that appear in $k-$generaliz...

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Autores:
Bravo, Jhon J.
Luca, Florian
Tipo de recurso:
Article of journal
Fecha de publicación:
2012
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
spa
OAI Identifier:
oai:repositorio.unal.edu.co:unal/42254
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/42254
http://bdigital.unal.edu.co/32351/
Palabra clave:
Fibonacci numbers
Lower bounds for nonzero linear forms in logarithms of algebraic numbers
11B39
11J86
Rights
openAccess
License
Atribución-NoComercial 4.0 Internacional
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spelling Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Bravo, Jhon J.738072e5-6106-4cb9-8ad0-dbdce4271231300Luca, Florian630d8bca-04a0-468c-a413-c9ca1f667e903002019-06-28T10:39:38Z2019-06-28T10:39:38Z2012https://repositorio.unal.edu.co/handle/unal/42254http://bdigital.unal.edu.co/32351/The $k-$generalized Fibonacci sequence $\big(F_{n}^{(k)}\big)_{n}$ resembles the Fibonacci sequence in that it starts with $0,\ldots,0,1$ ($k$ terms) and each term afterwards is the sum of the $k$ preceding terms. In this paper, we are interested in finding powers of two that appear in $k-$generalized Fibonacci sequences; i.e., we study the Diophantine equation $F_n^{(k)}=2^m$ in positive integers $n,k,m$ with $k\geq 2$.application/pdfspaUniversidad Nacuional de Colombia; Sociedad Colombiana de matemáticashttp://revistas.unal.edu.co/index.php/recolma/article/view/31844Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de MatemáticasRevista Colombiana de MatemáticasRevista Colombiana de Matemáticas; Vol. 46, núm. 1 (2012); 67-79 0034-7426Bravo, Jhon J. and Luca, Florian (2012) Powers of two in generalized fibonacci sequences. Revista Colombiana de Matemáticas; Vol. 46, núm. 1 (2012); 67-79 0034-7426 .Powers of two in generalized fibonacci sequencesArtículo de revistainfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/ARTFibonacci numbersLower bounds for nonzero linear forms in logarithms of algebraic numbers11B3911J86ORIGINAL31844-116372-1-PB.pdfapplication/pdf420964https://repositorio.unal.edu.co/bitstream/unal/42254/1/31844-116372-1-PB.pdf795a520356b73cfede862432193cbc22MD5131844-142400-1-PB.htmltext/html4413https://repositorio.unal.edu.co/bitstream/unal/42254/2/31844-142400-1-PB.htmlb13221f1824b2bb8aedb7622f9f5e69eMD52THUMBNAIL31844-116372-1-PB.pdf.jpg31844-116372-1-PB.pdf.jpgGenerated Thumbnailimage/jpeg4802https://repositorio.unal.edu.co/bitstream/unal/42254/3/31844-116372-1-PB.pdf.jpgde82ba77bd7b42551eca87e609259bd2MD53unal/42254oai:repositorio.unal.edu.co:unal/422542024-02-04 23:06:23.538Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co
dc.title.spa.fl_str_mv Powers of two in generalized fibonacci sequences
title Powers of two in generalized fibonacci sequences
spellingShingle Powers of two in generalized fibonacci sequences
Fibonacci numbers
Lower bounds for nonzero linear forms in logarithms of algebraic numbers
11B39
11J86
title_short Powers of two in generalized fibonacci sequences
title_full Powers of two in generalized fibonacci sequences
title_fullStr Powers of two in generalized fibonacci sequences
title_full_unstemmed Powers of two in generalized fibonacci sequences
title_sort Powers of two in generalized fibonacci sequences
dc.creator.fl_str_mv Bravo, Jhon J.
Luca, Florian
dc.contributor.author.spa.fl_str_mv Bravo, Jhon J.
Luca, Florian
dc.subject.proposal.spa.fl_str_mv Fibonacci numbers
Lower bounds for nonzero linear forms in logarithms of algebraic numbers
11B39
11J86
topic Fibonacci numbers
Lower bounds for nonzero linear forms in logarithms of algebraic numbers
11B39
11J86
description The $k-$generalized Fibonacci sequence $\big(F_{n}^{(k)}\big)_{n}$ resembles the Fibonacci sequence in that it starts with $0,\ldots,0,1$ ($k$ terms) and each term afterwards is the sum of the $k$ preceding terms. In this paper, we are interested in finding powers of two that appear in $k-$generalized Fibonacci sequences; i.e., we study the Diophantine equation $F_n^{(k)}=2^m$ in positive integers $n,k,m$ with $k\geq 2$.
publishDate 2012
dc.date.issued.spa.fl_str_mv 2012
dc.date.accessioned.spa.fl_str_mv 2019-06-28T10:39:38Z
dc.date.available.spa.fl_str_mv 2019-06-28T10:39:38Z
dc.type.spa.fl_str_mv Artículo de revista
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dc.relation.spa.fl_str_mv http://revistas.unal.edu.co/index.php/recolma/article/view/31844
dc.relation.ispartof.spa.fl_str_mv Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de Matemáticas
Revista Colombiana de Matemáticas
dc.relation.ispartofseries.none.fl_str_mv Revista Colombiana de Matemáticas; Vol. 46, núm. 1 (2012); 67-79 0034-7426
dc.relation.references.spa.fl_str_mv Bravo, Jhon J. and Luca, Florian (2012) Powers of two in generalized fibonacci sequences. Revista Colombiana de Matemáticas; Vol. 46, núm. 1 (2012); 67-79 0034-7426 .
dc.rights.spa.fl_str_mv Derechos reservados - Universidad Nacional de Colombia
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dc.rights.license.spa.fl_str_mv Atribución-NoComercial 4.0 Internacional
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rights_invalid_str_mv Atribución-NoComercial 4.0 Internacional
Derechos reservados - Universidad Nacional de Colombia
http://creativecommons.org/licenses/by-nc/4.0/
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
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dc.publisher.spa.fl_str_mv Universidad Nacuional de Colombia; Sociedad Colombiana de matemáticas
institution Universidad Nacional de Colombia
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