Introduction to number theory (Berkeley Math 115) - Introduction to number theory lecture 16. More numerical calculation

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 give some more examples of numerical algorithms, such as as algorithm to find square roots of -1, and a factoring algorithm, and a prime testing algorithm that works on some Carmichael numbers. The textbook is "An introduction to the theory of numbers" by Niven, Zuckerman, and Montgomery (5th edition).