An Algorithm to Solve a Pell Equation

Given a non-square positive integer n, we want to find two integers x and y such that x² -- ny² = ±1. We present an elementary method to do this and we make the well-known link with the continued fraction of √n with a new pedagogical point of view. Finally we give a generalization to deal with equations mx² -- ny² = ± 1 when m and n are positive integers whose product is not a perfect square.