Elementary Number Theory

by Stein, William

• ISBN13: 9780387855240
• ISBN10: 0387855246
• eBook ISBN(s): 9780387855257
• Format: Hardcover
• Copyright: 2009-01-02
• Publisher: SPRINGER - VERLAG
• More Book Details

Summary

This is a textbook about classical elementary number theory and elliptic curves. The first part discusses elementary topics such as primes, factorization, continued fractions, and quadratic forms, in the context of cryptography, computation, and deep open research problems. The second part is about elliptic curves, their applications to algorithmic problems, and their connections with problems in number theory such as Fermat's Last Theorem, the Congruent Number Problem, and the Conjecture of Birch and Swinnerton-Dyer. The intended audience of this book is an undergraduate with some familiarity with basic abstract algebra, e.g. rings, fields, and finite abelian groups.

Author Biography

William Stein is an Associate Professor of Mathematics at the University of Washington.

Table of Contents

Prime numbers	p. 1
The ring of integers modulo n	p. 21
Public-key cryptography	p. 49
Quadratic reciprocity	p. 69
Continued fractions	p. 93
Elliptic curves	p. 123
Answers and hints	p. 149
References	p. 155
Index	p. 161
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