posted 6 Jan 2022

Number Theory

§ Overview

The study of the natural numbers. Notes from Rosen and Ireland's A Classical Introduction to Modern Number Theory.

(16 Jan 2025): I've updated my site to a different framework; so I had to change how I do things.

The numberings of thorems, propositions, lemmas, etc. are now incorrect as a result.

I probably won't be readding most of the pages under this topic.

§ Contents

6 Jan 2022

Unique Factorization in $\mathbb{Z}$

6 Jan 2022

Unique Factorization in $k[x]$

6 Jan 2022

Unique Factorization in a Principal Ideal Domain

6 Jan 2022

$\mathbb{Z}[i]$ and $\mathbb{Z}[\omega]$ are Euclidean Domains

6 Jan 2022

Chapter 1 Exercises

8 Jan 2022

Number Theory

§ Overview

§ Contents

Unique Factorization in Z\mathbb{Z}Z

Unique Factorization in k[x]k[x]k[x]

Unique Factorization in a Principal Ideal Domain

Z[i]\mathbb{Z}[i]Z[i] and Z[ω]\mathbb{Z}[\omega]Z[ω] are Euclidean Domains

Chapter 1 Exercises

The Infinitude of Primes

Unique Factorization in $\mathbb{Z}$

Unique Factorization in $k[x]$

$\mathbb{Z}[i]$ and $\mathbb{Z}[\omega]$ are Euclidean Domains