Fermat's Last Theorem: A Genetic Introduction to Algebraic Number Theory (Graduate Texts in Mathematics, 50)

Fermat's Last Theorem: A Genetic Introduction to Algebraic Number Theory (Graduate Texts in Mathematics, 50) by Edwards, Harold M.. Paperback edition. ISBN: 9780387950020.

This book is an introduction to algebraic number theory via the famous problem of "Fermats Last Theorem." The exposition follows the historical development of the problem, beginning with the work of Fermat and ending with Kummers 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 Eulers 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 Kummers 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.