Introduction to number theory (Berkeley Math 115) - Introduction to number theory lecture 37 Continued fractions

This lecture is part of my Berkeley math 115 course "Introduction to number theory" For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj53L8sMbzIhhXSAOpuZ1Fov8 We show how to used continued fractions to find rationalapproximations to real numbers and to soleve the Pellian equation. The textbook is "An introduction to the theory of numbers" by Niven, Zuckerman, and Montgomery (5th edition).