Sistemas de equações diofantinas lineares

• Autor(a) principal: Santos Neto, José Antônio
• 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
• 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

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.