Matibe, Vhuhwavho2020-02-122020-02-122019https://hdl.handle.net/10539/28866A Dissertation Submitted to the Faculty of Science at The University of Witwatersrand to fulfillment of the Requirements for the Degree of Master of Science School of Mathematics March 2019The aim of this dissertation is to explore the Pell equation, through studying one method of solving it that is believed to have been initially used to nd good approximations to the square root of square free positive integers, namely the continued fraction [8]. We further look at its signi cance by considering a number of its applications.enThesis