This book is a concise introduction to number theory and some related algebra, with an emphasis on solving equations in integers. This is the only elementary number theory book that includes significant applications of ideal theory. It is clearly written, well illustrated, and supplied with carefully designed exercises, making it a pleasure to use as an undergraduate textbook or for independent study.

Includes supplementary material: sn.pub/extras

Autorentext

John Stillwell is a professor of mathematics at the University of San Francisco. He is also an accomplished author, having published several books with Springer, including The Four Pillars of Geometry; Elements of Algebra; Numbers and Geometry; and many more.

Inhalt
1 Natural numbers and integers.- 2 The Euclidean algorithm.- 3 Congruence arithmetic.- 4 The RSA cryptosystem.- 5 The Pell equation.- 6 The Gaussian integers.- 7 Quadratic integers.- 8 The four square theorem.- 9 Quadratic reciprocity.- 10 Rings.- 11 Ideals.- 12 Prime ideals.