ABSTRACT
Up to now, we have been studying the set https://www.w3.org/1998/Math/MathML"> ℤ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003318712/0a8d6242-fb38-4fc0-af6c-0a4803a1cbee/content/C007_equ_0001.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> integers. In this chapter, however, we expand our horizons and study other number systems that have features in common with https://www.w3.org/1998/Math/MathML"> ℤ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003318712/0a8d6242-fb38-4fc0-af6c-0a4803a1cbee/content/C007_equ_0001.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> , but also some differences as well. We study them for several reasons. First, we can use these systems to actually prove things about the integers, and second, their study helps shed some light on unique factorization into primes, which turns out to be a subtler idea than one might expect at first.
