ABSTRACT
In this chapter, the authors provide various applications where they arise naturally when looking at problems involving the usual integers. They aim to prove that every nonzero Gaussian integer is either a unit, an irreducible, or a product of irreducibles, and that this factorization is unique. The Gaussian integers have many properties in common with the integers and can be studied in their own right. When proved that integers factor uniquely as products of primes, it was easy to show that every integer factors into a product of primes. Uniqueness was the difficult part and used the Division Algorithm to show this. The authors explore the same situation in the Gaussian integers: factorization is easy, uniqueness is more difficult. They deal with factorization into irreducibles as their first order of business. The authors show how the Gaussian integers can be used to derive information about integers.
