Uma introdução ao estudo de equações diofantinas lineares para o ensino médio

Abstract

The main objective of this work is to show the viability of applying the study of Linear Diophantine Equations in High School classes. For that, it is necessary some knowledge of Theory of Numbers that can be introduced based on Elementary School contents, such as Greatest Common Divisor, Euclid’s algorithm, divisibility and division algorithm. Some others will be introduced, such as the congruence study, which is related to the remains of the Euclidean division. In the first chapters, a basis on Elementary Theory of Numbers will be presented, as they are essential in the resolution of Linear Diophantine Equations. Emphasis will be placed on solving linear Diophantine equations in some everyday problems, however, it is essential to present elementary methods for solving some types of non-linear Diophantine equations, such as factorization and the use of inequalities. The purpose is to show that the introduction to problem solving by means of Linear Diophantine Equations in two unknowns does not require advanced knowledge, allowing it to be done in High School