Solving Pell's equation with continued fractions

In this report we will use continued fractions to solve Fell's equation We explore some of the properties of simple continued fractions, discuss the relationship between reduced quadratic irrationals and purely periodic simple continued fractions and then give the solution to Fell's and the negative Pell equation. We close by summarizing the entire process in the PQa algorithm which also shows us how to solve some Pell-like equations.