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).