Elements of Number Theory

This book is a concise introduction to number theory and some related algebrawith an emphasis on solving equations in integers. Finding integer solutionsled to ... » 

This book is a concise introduction to number theory and some related algebrawith an emphasis on solving equations in integers. Finding integer solutionsled to two fundamental ideas of number theory in ancient times the Euclideanalgorithm and unique prime factorization and in modern times to twofundamental ideas of algebra rings and ideals. The development of theseideas and the transition from ancient to modern is the main theme of thebook. The historical development has been followed where it helps to motivatethe introduction of new concepts but modern proofs have been used where theyare simpler more natural or more interesting. These include some that havenot yet appeared in textbooks such as a treatment of the Pell equation usingConways theory of quadratic forms. Also this is the only elementary numbertheory book that includes significant applications of ideal theory. It isclearly written well illustrated and supplied with carefully designedexercises making it a pleasure to use as an undergraduate textbook or forindependent study. John Stillwell is Professor of Mathematics at the Universityof San Francisco. He is the author of several highly regarded books publishedby SpringerVerlag including Mathematics and Its History Second Edition2001 Numbers and Geometry 1997 and Elements of Algebra 1994. TOC Preface Natural numbers and integers The Euclidean algorithm Congruencearithmetic The RSA cryptosystem The Pell equation The Gaussian Integers Quadratic integers The four square theorem Quadratic reciprocity Rings Ideals Prime ideals Bibliography Index «