Introduction to number theory (Berkeley Math 115) - Introduction to number theory lecture 19. Hensel and Newton's method

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 describe a method due to Hensel and Newton for lifting a solution of an equation mod p to a solution mod a power of p. The textbook is "An introduction to the theory of numbers" by Niven, Zuckerman, and Montgomery (5th edition).