Equações diofantinas e o método das secantes e tangentes de Fermat

Abstract

Over the past decades, the transmission of mathematical knowledge in basic education has undergone several changes. The “Teaching Traditional” math was based on memorizing formulas, so there mechanization in problem solving where the student was seen as a liability to be process. The new vision of education that seeks to signify exposed to room content, motivated the choice of this theme, as diophantine equations involving situations problems can be easily noticed in our daily lives. The objective of this work is an opportunity for a realization of an advisory reading for the teacher of basic education, and assert that these equations can be applied in basic education as a tool that encourages the logical thinking, reasoning, understanding and mathematical interpretation. The formulation of this material which is divided into five chapters was through literature review through descriptive research. The introduction comprises the first chapter. The second chapter deals with the Legacy of Diophantus: life and works, emphasizing his work entitled “Arithmetica” which contributed significantly to the development of number theory. The third chapter deals with linear Diophantine equations in n variables. The fourth chapter discusses the Pythagorean tender, Fermat’s of secants and Tangents method, in finding rational solutions to equations with rational coefficients, of the form ax2 + by2 = c and a particular case Fermat’s Last Theorem. The fifth chapter is composed of problems on linear diophantine equations.