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 Professor Emeritus at the University of San Francisco and formerly Associate Professor at Monash University in Melbourne, Australia. He is an accomplished author, whose Springer books include: The Four Pillars of Geometry, Elements of Algebra, Naive Lie Theory, 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.