Convite às equações diofantinas: uma abordagem para a educação básica

Abstract

In this dissertation, the results of a wide bibliographic research about Diophantine equa- tions and their most used solution methods are exposed. The simplest equation of these class is the one in the form ax + by = c, with a, b and c integers numbers and ab /= 0, called Diophantine linear equation in the unknowns x and y. Divers solutions methods for these equations, in two or three unknowns are discussed. Therefore, concepts like divisi- bility, Euclidean division, grated common divisor, prime numbers, among others, that are included in the Elementary School’s curriculum. In Brazil, Diophantine equations are not commonly exploited in Basic Education, even though they are perfectly understandable at this educational level, like Professor A. Guelfond shows in his book consulted in the redaction of the dissertation. There are also a chapter about Diophantus’s contributions to Arithmetic, which can be a source of motivation to study the Diophantine equations; and another chapter, extending perspectives, about nonlinear Diophantine equations. We hope that the dissertation becomes a suitable easy accessible bibliographic font for Basic Education teachers and stimulates their interest and creativity for an elemental introducing of these contents in their teaching and in the student’s training for Math Olympiads.