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Elements of Number Theory

Elements of Number Theory - 02 edition

ISBN13: 978-0387955872

Cover of Elements of Number Theory 02 (ISBN 978-0387955872)
ISBN13: 978-0387955872
ISBN10: 0387955879
Cover type:
Edition/Copyright: 02
Publisher: Springer-Verlag New York
Published: 2002
International: No
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Elements of Number Theory - 02 edition

ISBN13: 978-0387955872

John Stillwell

ISBN13: 978-0387955872
ISBN10: 0387955879
Cover type:
Edition/Copyright: 02
Publisher: Springer-Verlag New York

Published: 2002
International: No
Summary

This book is a concise introduction to number theory and some related algebra, with an emphasis on solving equations in integers. Finding integer solutions led to two fundamental ideas of number theory in ancient times - the Euclidean algorithm and unique prime factorization - and in modern times to two fundamental ideas of algebra - rings and ideals. The development of these ideas, and the transition from ancient to modern, is the main theme of the book. The historical development has been followed where it helps to motivate the introduction of new concepts, but modern proofs have been used where they are simpler, more natural, or more interesting. These include some that have not yet appeared in textbooks, such as a treatment of the Pell equation using Conway's theory of quadratic forms. Also, 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.

Table of Contents

Natural numbers and integers
The Euclidean algorithm
Congruence arithmetic
The RSA cryptosystem
The Pell equation
The Gaussian Integers
Quadratic integers
The four square theorem
Quadratic reciprocity
Rings
Ideals
Prime ideals
Bibliography
Index

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