Introduction to number theory (Berkeley Math 115) - Introduction to number theory lecture 10. Fermat's theorem

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 prove Fermat's theorem about powers mod p. The textbook is "An introduction to the theory of numbers" by Niven, Zuckerman, and Montgomery (5th edition).