Equações diofantinas não lineares: uma proposta didática para resolução de problemas

Abstract

This dissertation aims to present didactic proposals that help to fix and apply basic arithmetic contents through George Pólya's methods for solving problems involving nonlinear Diophantine equations. A Diophantine equation is an algebraic equation whose unknowns represent integers. The solution methods of the equations treated here require knowledge of basic facts about remarkable products, congruences, analytic geometry, and metric relationships in the triangle. Since the problems are independent, it can be used by the teacher separately in different classes and levels of education. The work culminates with a proposal of didactic sequences for application of problem solving in the classroom.