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

This introduction to algebraic number theory via the famous problem of "Fermats Last Theorem" follows its historical development, beginning with the work of Fermat and ending with Kummers theory of "ideal" factorization. The more elementary topics, such as Eulers proof of the impossibilty of x+y=z, are treated in an uncomplicated 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 theory to quadratic integers and relates this to Gauss'theory of binary quadratic forms, an interesting and important connection that is not explored in any other book. "...this softcover version of the bestseller follows the work of early influential number theorists in this intriguing adventure for proof of Fermat's Last Theorem." Work on this book was supported in part by the James M. Vaughn, Jr., Vaughn Foundation Fund. When Pierre de Fermat died in 1665 he was one of the most famous mathematicians in Europe.