# An Introduction to Number Theory

Part of the Graduate Texts in Mathematics book series (GTM, volume 232)

Part of the Graduate Texts in Mathematics book series (GTM, volume 232)

An Introduction to Number Theory provides an introduction to the main streams of number theory. Starting with the unique factorization property of the integers, the theme of factorization is revisited several times throughout the book to illustrate how the ideas handed down from Euclid continue to reverberate through the subject.

In particular, the book shows how the Fundamental Theorem of Arithmetic, handed down from antiquity, informs much of the teaching of modern number theory. The result is that number theory will be understood, not as a collection of tricks and isolated results, but as a coherent and interconnected theory.

A number of different approaches to number theory are presented, and the different streams in the book are brought together in a chapter that describes the class number formula for quadratic fields and the famous conjectures of Birch and Swinnerton-Dyer. The final chapter introduces some of the main ideas behind modern computational number theory and its applications in cryptography.

Written for graduate and advanced undergraduate students of mathematics, this text will also appeal to students in cognate subjects who wish to be introduced to some of the main themes in number theory.

Arithmetic Prime Prime numbers Riemann zeta function cryptography number theory

- DOI https://doi.org/10.1007/b137432
- Copyright Information Springer-Verlag London Limited 2005
- Publisher Name Springer, London
- eBook Packages Mathematics and Statistics
- Print ISBN 978-1-85233-917-3
- Online ISBN 978-1-84628-044-3
- Series Print ISSN 0072-5285
- About this book

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