Frações contínuas para a resolução da equação de Pell

Abstract

The rational and irrational numbers present little research in basic education and, when they are approached, they are usually presented with a focus on privileging only operational, finite, infinite and exact aspects, which limits the approach and understanding of this important theme in the teaching of Mathematics. In this paper we will show how we can use the concept of Continuous Fractions to find whole solutions to Pell’s equations of the type x – dy = m, where m is an integer and d is a natural number null and not a perfect square. We will use the Geogebra software to visualize the positions of the solution.