Sistemas de equações diofantinas lineares

• Ano de defesa: 2021
• Autor(a) principal: Santos Neto, José Antônio
• Orientador(a): Cardoso, José Anderson Valença
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Programa de Pós-Graduação: Mestrado Profissional em Matemática
• Palavras-chave em Português: Equações diofantinas; Aritmética; Matrizes; Algorítmos; Aritmética dos inteiros; Equações diofantinas generalizadas; Matrizes unimodulares; Sistemas de equações diofantinas lineares; Algoritmo de Euclides estendido generalizado
• Palavras-chave em Inglês: Integer arithmetic; Generalized Diophantine equations; Unimodular matrices; Linear Diophantine equation systems; Generalized extended euclidean algorithm
• Área do conhecimento CNPq: CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://ri.ufs.br/jspui/handle/riufs/18064

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.