Congruência modular : uma proposta didática para a resolução de equações diofantinas lineares

Abstract

This study aims to provide theoretical and practical support for students and teachers, with the goal of enhancing their understanding, interpretation, and problem solving skills regarding issues that can be addressed through linear Diophantine equations. It presents modular congruence as an alternative, valuable, and complementary tool to the Euclidean algorithm for this purpose. To achieve this, essential topics will be covered to facilitate comprehension of the relevant concepts within the pedagogical framework, including: integers and their operations, divisibility, Euclidean division, greatest common divisor, the Euclidean algorithm, and fundamental concepts of modular arithmetic. In parallel, we seek to develop educational games as a supplementary resource for teachers who wish to introduce the study of Diophantine equations in basic education. This initiative is based on the premise that the intentional use of games in mathematics education can create a stimulating and challenging environment, fostering the development of logical thinking, cooperative skills, and the construction of mathematical concepts. We understand that games serve as facilitators of learning by incorporating a playful dimension into problem-solving, providing students with a conducive environment for concept assimilation, even when formalization has occurred beforehand.