Fermat's Last Theorem: A Genetic Introduction to Algebraic Number Theory

by Edwards, Harold M.; Axler, S.; Gehring, F. W.; Ribet, K. A.

• ISBN13: 9780387950020
• ISBN10: 0387950028
• Format: Paperback
• Copyright: 2000-01-01
• Publisher: Springer Verlag

Summary

This book is an introduction to algebraic number theory via the famous problem of "Fermat's Last Theorem." The exposition follows the historical development of the problem, beginning with the work of Fermat and ending with Kummer's theory of "ideal" factorization, by means of which the theorem is proved for all prime exponents less than 37. The more elementary topics, such as Euler's proof of the impossibilty of x+y=z, are treated in an elementary way, and new concepts and techniques are introduced only after having been motivated by specific problems. The book also covers in detail the application of Kummer's ideal theory to quadratic integers and relates this theory to Gauss' theory of binary quadratic forms, an interesting and important connection that is not explored in any other book.

Table of Contents

Fermat	1	(38)
Euler	39	(20)
From Euler to Kummer	59	(17)
Kummer's theory of ideal factors	76	(76)
Fermat's Last Theorem for regular primes	152	(29)
Determination of the class number	181	(64)
Divisor theory for quadratic integers	245	(60)
Gauss's theory of binary quadratic forms	305	(37)
Dirichlet's class number formula	342	(30)
Appendix: The natural numbers	372	(9)
Answers to exercises	381	(22)
Bibliography	403	(6)
Index	409