Elements of Number Theory

Focusing on integer solutions to polynomial equations, this book delves into the interplay between number theory and algebra, particularly through the concepts of rings and ideals. It builds upon the foundational work of Galois, Kummer, and Dedekind, illustrating how these algebraic structures arise from number theory. By exploring the failures of unique prime factorization, it highlights the historical development of "ideal numbers" and their significance in understanding the algebraic properties of integers. This work serves as a comprehensive introduction to key ideas in number theory.