Complex Numbers: Gauss Numbers

This lecture explores the concept of Gaussian integers, introduced by Gauss, where prime numbers in the set of natural numbers may not remain prime when considering complex numbers with integer coefficients. The lecture delves into the definition of Gaussian integers, their properties, and the factorization of numbers of this type. Through examples, it illustrates how certain prime numbers can be factorized in the Gaussian integers set, highlighting the distinction between primes that remain prime and those that do not. Additionally, it discusses a theorem in number theory that determines which prime numbers can be expressed as the sum of two integer squares.