Equações diofantinas lineares: um aplicativo para a resolução

• Autor(a) principal: Santos, Lucas Azevedo dos [UNESP]
• Data de Publicação: 2016
• Tipo de documento: Trabalho de conclusão de curso
• Idioma: por
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://hdl.handle.net/11449/155325; http://www.athena.biblioteca.unesp.br/exlibris/bd/capelo/2017-04-19/000881714.pdf
• topic: Equações lineares; Andróides; Algoritmos; Androids

A Diophantine equation is a polynomial equation with the restriction which each of its coefficients must be integers. These equations are mostly found in everyday issues, and nowadays, in several areas of computer science. Taking this as a premise, this work aims at the implementation of technics for solving Diophantine equations in a computer program. To accomplish this goal, a revision in the history of the theory of the numbers is made, highlighting the main mathematicians who contributed for this theory, from the ancient Greece until modernity. A revision of the theory of the numbers itself is also made, where key concepts for resolving Diophantine equations are studied. After explaining the method for solving Diophantine equations, a revision in already existing programs which make this resolution is made, and then, a program for the Android platform is implemented. The main features of this program are analysed and exposed. The conclusion of this work is the importance of the theoretical and historical basis for a better understanding in solving Diophantine equations, as well as its importance in the world nowadays. The focus of this work are linear Diophantine equations with two variables