Counting integers representable as images of polynomials modulo n

Given a polynomial f(x1,x2,…,xt) in t variables with integer coefficients and a positive integer n, let α(n) be the number of integers 0 ≤ a < n such that the polynomialcongruencef(x1,x2,…,xt) ≡ a(modn)issolvable. Wedescribeamethod that allows us to determine the function α associated with polyno...

Full description

Autores:
Arias, Fabián
Borja, Jerson
Rubio, Luis
Tipo de recurso:
Fecha de publicación:
2019
Institución:
Universidad Tecnológica de Bolívar
Repositorio:
Repositorio Institucional UTB
Idioma:
eng
OAI Identifier:
oai:repositorio.utb.edu.co:20.500.12585/12340
Acceso en línea:
https://hdl.handle.net/20.500.12585/12340
https://cs.uwaterloo.ca/journals/JIS/
Palabra clave:
Diophantine Equation;
Number;
Linear Forms in Logarithms
LEMB
Rights
openAccess
License
http://creativecommons.org/licenses/by-nc-nd/4.0/
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network_acronym_str UTB2
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repository_id_str
dc.title.spa.fl_str_mv Counting integers representable as images of polynomials modulo n
title Counting integers representable as images of polynomials modulo n
spellingShingle Counting integers representable as images of polynomials modulo n
Diophantine Equation;
Number;
Linear Forms in Logarithms
LEMB
title_short Counting integers representable as images of polynomials modulo n
title_full Counting integers representable as images of polynomials modulo n
title_fullStr Counting integers representable as images of polynomials modulo n
title_full_unstemmed Counting integers representable as images of polynomials modulo n
title_sort Counting integers representable as images of polynomials modulo n
dc.creator.fl_str_mv Arias, Fabián
Borja, Jerson
Rubio, Luis
dc.contributor.author.none.fl_str_mv Arias, Fabián
Borja, Jerson
Rubio, Luis
dc.subject.keywords.spa.fl_str_mv Diophantine Equation;
Number;
Linear Forms in Logarithms
topic Diophantine Equation;
Number;
Linear Forms in Logarithms
LEMB
dc.subject.armarc.none.fl_str_mv LEMB
description Given a polynomial f(x1,x2,…,xt) in t variables with integer coefficients and a positive integer n, let α(n) be the number of integers 0 ≤ a < n such that the polynomialcongruencef(x1,x2,…,xt) ≡ a(modn)issolvable. Wedescribeamethod that allows us to determine the function α associated with polynomials of the form c1xk1+c2xk2+···+ctxkt. Then, we apply this method to polynomials that involve sums and differences of squares, mainly to the polynomials x2 +y2, x2 −y2, and x2 +y2 +z2. © 2019, University of Waterloo. All rights reserved.
publishDate 2019
dc.date.issued.none.fl_str_mv 2019
dc.date.accessioned.none.fl_str_mv 2023-07-21T16:24:19Z
dc.date.available.none.fl_str_mv 2023-07-21T16:24:19Z
dc.date.submitted.none.fl_str_mv 2023
dc.type.coarversion.fl_str_mv http://purl.org/coar/version/c_b1a7d7d4d402bcce
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dc.type.driver.spa.fl_str_mv info:eu-repo/semantics/article
dc.type.hasversion.spa.fl_str_mv info:eu-repo/semantics/draft
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status_str draft
dc.identifier.citation.spa.fl_str_mv Arias, F., Borja, J., & Rubio, L. (2018). Counting integers representable as images of polynomials modulo $ n$. arXiv preprint arXiv:1812.11599.
dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/20.500.12585/12340
dc.identifier.url.none.fl_str_mv https://cs.uwaterloo.ca/journals/JIS/
dc.identifier.instname.spa.fl_str_mv Universidad Tecnológica de Bolívar
dc.identifier.reponame.spa.fl_str_mv Repositorio Universidad Tecnológica de Bolívar
identifier_str_mv Arias, F., Borja, J., & Rubio, L. (2018). Counting integers representable as images of polynomials modulo $ n$. arXiv preprint arXiv:1812.11599.
Universidad Tecnológica de Bolívar
Repositorio Universidad Tecnológica de Bolívar
url https://hdl.handle.net/20.500.12585/12340
https://cs.uwaterloo.ca/journals/JIS/
dc.language.iso.spa.fl_str_mv eng
language eng
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dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
dc.rights.cc.*.fl_str_mv Attribution-NonCommercial-NoDerivatives 4.0 Internacional
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-nd/4.0/
Attribution-NonCommercial-NoDerivatives 4.0 Internacional
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.extent.none.fl_str_mv 15 páginas
dc.format.mimetype.spa.fl_str_mv application/pdf
dc.publisher.place.spa.fl_str_mv Cartagena de Indias
dc.source.spa.fl_str_mv Journal of Integer Sequences
institution Universidad Tecnológica de Bolívar
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spelling Arias, Fabián510f8ed3-96f5-410f-81e4-c14e21e69c57Borja, Jerson6e810ab4-1ee6-4582-917f-958468bdb2fcRubio, Luis334955b7-098b-462f-9566-108e222a2ede2023-07-21T16:24:19Z2023-07-21T16:24:19Z20192023Arias, F., Borja, J., & Rubio, L. (2018). Counting integers representable as images of polynomials modulo $ n$. arXiv preprint arXiv:1812.11599.https://hdl.handle.net/20.500.12585/12340https://cs.uwaterloo.ca/journals/JIS/Universidad Tecnológica de BolívarRepositorio Universidad Tecnológica de BolívarGiven a polynomial f(x1,x2,…,xt) in t variables with integer coefficients and a positive integer n, let α(n) be the number of integers 0 ≤ a < n such that the polynomialcongruencef(x1,x2,…,xt) ≡ a(modn)issolvable. Wedescribeamethod that allows us to determine the function α associated with polynomials of the form c1xk1+c2xk2+···+ctxkt. Then, we apply this method to polynomials that involve sums and differences of squares, mainly to the polynomials x2 +y2, x2 −y2, and x2 +y2 +z2. © 2019, University of Waterloo. All rights reserved.15 páginasapplication/pdfenghttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://purl.org/coar/access_right/c_abf2Journal of Integer SequencesCounting integers representable as images of polynomials modulo ninfo:eu-repo/semantics/articleinfo:eu-repo/semantics/drafthttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/version/c_b1a7d7d4d402bccehttp://purl.org/coar/resource_type/c_2df8fbb1Diophantine Equation;Number;Linear Forms in LogarithmsLEMBCartagena de IndiasBurton, D.M. (2011) Elementary Number Theory. Cited 533 times. 7th ed., McGraw-HillBroughan, K.A. Characterizing the sum of two cubes (2003) Journal of Integer Sequences, 6 (4). Cited 5 times. http://www.cs.uwaterloo.ca/journals/JIS/VOL6/Broughan/broughan25.pdfBurns, R. (2017) Representing Numbers as the Sum of Squares and Powers in the Ring Zn, Preprint https://arxiv.org/abs/1708.03930Harrington, J., Jones, L., Lamarche, A. Representing integers as the sum of two squares in the ring ℤn (2014) Journal of Integer Sequences, 17 (7), art. no. 14.7.4. Cited 2 times. https://cs.uwaterloo.ca/journals/JIS/VOL17/Jones/jones14.pdfIreland, K., Rosen, M. (1990) A Classical Introduction to Modern Number Theory. Cited 1496 times. 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