Fermat's Theorem: Sums of Squares

This lecture covers Fermat's Theorem from 1640, stating that a non-zero integer can be represented as a sum of two squares if certain conditions are met. It delves into the factorization of integers, the properties of the ring Z[i], and the Hurwitz quaternions. The lecture also explores the concept of reduced trace and norm, the polarization of quaternions, and the properties of the Hurwitz quaternions ring.