Theory of numbers: Gauss's lemma
Channel: Richard E Borcherds
Date: 2021-02-11

This lecture is part of an online undergraduate course on the theory of numbers.

We describe Gauss's lemma which gives a useful criterion for whether a number n is a quadratic residue of a prime p. We work it out explicitly for n = -1, 2 and 3, and as an application prove some cases of Dirichlet's theorem. Finally we use it to show that the Legendre symbol (n/p) for fixed n depends only on p mod 4n. 



For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj52Qf7lc3HHvHRdIysxEcj1H