Sistemas de equações diofantinas lineares
Autor(a) principal: | |
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Data de Publicação: | 2021 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Repositório Institucional da UFS |
Texto Completo: | https://ri.ufs.br/jspui/handle/riufs/18064 |
Resumo: | The present work has as main objective to discuss and propose a method to find all possible solutions of the systems of linear equations, possible and indeterminate, with integer independent terms and coefficients, named here as systems of linear Diophantine equations. For this, it was necessary a previous study on divisibility, Euclidean division, maximum common divisor, Euclid’s algorithm and Diophantine equations, as well as the generalization of some concepts and results present in these topics. In addition, we review the basic contents of matrices and determinants, which are necessary in some demonstrations and to understand the proposed algorithm to solve these systems. |
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Santos Neto, José AntônioCardoso, José Anderson Valença2023-08-08T00:49:11Z2023-08-08T00:49:11Z2021-02-17SANTOS NETO, José Antônio. Sistemas de equações diofantinas lineares. 2021. 85 f. Dissertação (Mestrado Profissional em Matemática) - Universidade Federal de Sergipe, São Cristóvão, 2020.https://ri.ufs.br/jspui/handle/riufs/18064The present work has as main objective to discuss and propose a method to find all possible solutions of the systems of linear equations, possible and indeterminate, with integer independent terms and coefficients, named here as systems of linear Diophantine equations. For this, it was necessary a previous study on divisibility, Euclidean division, maximum common divisor, Euclid’s algorithm and Diophantine equations, as well as the generalization of some concepts and results present in these topics. In addition, we review the basic contents of matrices and determinants, which are necessary in some demonstrations and to understand the proposed algorithm to solve these systems.O presente trabalho tem como principal objetivo discutir e propor um método para encontrar todas as soluções inteiras dos sistemas de equações lineares, possíveis e indeterminados, com coeficientes e termos independentes inteiros, nomeados aqui de sistemas de equações Diofantinas lineares. Para tanto, foi necessário um prévio estudo sobre divisibilidade, divisão euclidiana, máximo divisor comum, algoritmo de Euclides e equações Diofantinas, bem como, a generalização de alguns conceitos e resultados presentes nesses tópicos. Além disso, revisamos os conteúdos básicos de matrizes e determinantes, os quais são necessários em algumas demonstrações e para compreensão do algoritmo proposto para solucionar os citados sistemas.São CristóvãoporEquações diofantinasAritméticaMatrizesAlgorítmosAritmética dos inteirosEquações diofantinas generalizadasMatrizes unimodularesSistemas de equações diofantinas linearesAlgoritmo de Euclides estendido generalizadoInteger arithmeticGeneralized Diophantine equationsUnimodular matricesLinear Diophantine equation systemsGeneralized extended euclidean algorithmCIENCIAS EXATAS E DA TERRA::MATEMATICASistemas de equações diofantinas linearesinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisMestrado Profissional em MatemáticaUniversidade Federal de Sergipe (UFS)reponame:Repositório Institucional da UFSinstname:Universidade Federal de Sergipe (UFS)instacron:UFSinfo:eu-repo/semantics/openAccessLICENSElicense.txtlicense.txttext/plain; charset=utf-81475https://ri.ufs.br/jspui/bitstream/riufs/18064/1/license.txt098cbbf65c2c15e1fb2e49c5d306a44cMD51ORIGINALJOSE_ANTONIO_SANTOS_NETO.pdfJOSE_ANTONIO_SANTOS_NETO.pdfapplication/pdf1375919https://ri.ufs.br/jspui/bitstream/riufs/18064/2/JOSE_ANTONIO_SANTOS_NETO.pdf3dc4d1b752ee79f0aa8a6e3597c4ec93MD52TEXTJOSE_ANTONIO_SANTOS_NETO.pdf.txtJOSE_ANTONIO_SANTOS_NETO.pdf.txtExtracted texttext/plain124201https://ri.ufs.br/jspui/bitstream/riufs/18064/3/JOSE_ANTONIO_SANTOS_NETO.pdf.txt65217bf3f672caa3c5e6f2a627459b35MD53THUMBNAILJOSE_ANTONIO_SANTOS_NETO.pdf.jpgJOSE_ANTONIO_SANTOS_NETO.pdf.jpgGenerated Thumbnailimage/jpeg1254https://ri.ufs.br/jspui/bitstream/riufs/18064/4/JOSE_ANTONIO_SANTOS_NETO.pdf.jpgae434ed58ff91e14a6c70d61d48006feMD54riufs/180642023-08-07 21:49:16.737oai:ufs.br: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Repositório InstitucionalPUBhttps://ri.ufs.br/oai/requestrepositorio@academico.ufs.bropendoar:2023-08-08T00:49:16Repositório Institucional da UFS - Universidade Federal de Sergipe (UFS)false |
dc.title.pt_BR.fl_str_mv |
Sistemas de equações diofantinas lineares |
title |
Sistemas de equações diofantinas lineares |
spellingShingle |
Sistemas de equações diofantinas lineares Santos Neto, José Antônio Equações diofantinas Aritmética Matrizes Algorítmos Aritmética dos inteiros Equações diofantinas generalizadas Matrizes unimodulares Sistemas de equações diofantinas lineares Algoritmo de Euclides estendido generalizado Integer arithmetic Generalized Diophantine equations Unimodular matrices Linear Diophantine equation systems Generalized extended euclidean algorithm CIENCIAS EXATAS E DA TERRA::MATEMATICA |
title_short |
Sistemas de equações diofantinas lineares |
title_full |
Sistemas de equações diofantinas lineares |
title_fullStr |
Sistemas de equações diofantinas lineares |
title_full_unstemmed |
Sistemas de equações diofantinas lineares |
title_sort |
Sistemas de equações diofantinas lineares |
author |
Santos Neto, José Antônio |
author_facet |
Santos Neto, José Antônio |
author_role |
author |
dc.contributor.author.fl_str_mv |
Santos Neto, José Antônio |
dc.contributor.advisor1.fl_str_mv |
Cardoso, José Anderson Valença |
contributor_str_mv |
Cardoso, José Anderson Valença |
dc.subject.por.fl_str_mv |
Equações diofantinas Aritmética Matrizes Algorítmos Aritmética dos inteiros Equações diofantinas generalizadas Matrizes unimodulares Sistemas de equações diofantinas lineares Algoritmo de Euclides estendido generalizado |
topic |
Equações diofantinas Aritmética Matrizes Algorítmos Aritmética dos inteiros Equações diofantinas generalizadas Matrizes unimodulares Sistemas de equações diofantinas lineares Algoritmo de Euclides estendido generalizado Integer arithmetic Generalized Diophantine equations Unimodular matrices Linear Diophantine equation systems Generalized extended euclidean algorithm CIENCIAS EXATAS E DA TERRA::MATEMATICA |
dc.subject.eng.fl_str_mv |
Integer arithmetic Generalized Diophantine equations Unimodular matrices Linear Diophantine equation systems Generalized extended euclidean algorithm |
dc.subject.cnpq.fl_str_mv |
CIENCIAS EXATAS E DA TERRA::MATEMATICA |
description |
The present work has as main objective to discuss and propose a method to find all possible solutions of the systems of linear equations, possible and indeterminate, with integer independent terms and coefficients, named here as systems of linear Diophantine equations. For this, it was necessary a previous study on divisibility, Euclidean division, maximum common divisor, Euclid’s algorithm and Diophantine equations, as well as the generalization of some concepts and results present in these topics. In addition, we review the basic contents of matrices and determinants, which are necessary in some demonstrations and to understand the proposed algorithm to solve these systems. |
publishDate |
2021 |
dc.date.issued.fl_str_mv |
2021-02-17 |
dc.date.accessioned.fl_str_mv |
2023-08-08T00:49:11Z |
dc.date.available.fl_str_mv |
2023-08-08T00:49:11Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/masterThesis |
format |
masterThesis |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
SANTOS NETO, José Antônio. Sistemas de equações diofantinas lineares. 2021. 85 f. Dissertação (Mestrado Profissional em Matemática) - Universidade Federal de Sergipe, São Cristóvão, 2020. |
dc.identifier.uri.fl_str_mv |
https://ri.ufs.br/jspui/handle/riufs/18064 |
identifier_str_mv |
SANTOS NETO, José Antônio. Sistemas de equações diofantinas lineares. 2021. 85 f. Dissertação (Mestrado Profissional em Matemática) - Universidade Federal de Sergipe, São Cristóvão, 2020. |
url |
https://ri.ufs.br/jspui/handle/riufs/18064 |
dc.language.iso.fl_str_mv |
por |
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por |
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openAccess |
dc.publisher.program.fl_str_mv |
Mestrado Profissional em Matemática |
dc.publisher.initials.fl_str_mv |
Universidade Federal de Sergipe (UFS) |
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