Introduction to number theory lecture 40. Examples of positive definite forms
Channel: Richard E Borcherds
Date: 2022-03-29

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 study some examples of positive defiite forms of small discriminant, and work out which primes they represent. For example we prove Fermat's theorem that any prime of the form 4n+1 is a sum of two squares. 

The textbook is "An introduction to the theory of numbers" by Niven, Zuckerman, and Montgomery (5th edition).