Algebraic Number Theory and Fermat's Last Theorem

Updated to reflect current research, Algebraic Number Theory and Fermat-s Last Theorem, Fourth Edition introduces fundamental ideas of algebraic numbers and explores one of the most intriguing stories in the history of mathematics-the quest for a proof of Fermat-s Last Theorem. The authors use this celebrated theorem to motivate a general study of the theory of algebraic numbers from a relatively concrete point of view. Students will see how Wiles-s proof of Fermat-s Last Theorem opened many new areas for future work.

New to the Fourth Edition

• Provides up-to-date information on unique prime factorization for real quadratic number fields, especially Harper-s proof that Z(v14) is Euclidean
• Presents an important new result: Mihailescu-s proof of the Catalan conjecture of 1844
• Revises and expands one chapter into two, covering classical ideas about modular functions and highlighting the new ideas of Frey, Wiles, and othe