Springer 17 Lectures on Fermat Numbers: From Number Theory to Geometry (CMS Books in Mathematics)

The pioneering work of Pierre de Fermat has attracted the attention of mathematicians for over 350 years. This book provides an overview of the many properties of Fermat numbers and demonstrates their applications in areas such as number theory, probability theory, geometry, and signal processing. It is an ideal introduction to the basic mathematical ideas and algebraic methods connected with the Fermat numbers. Review From the reviews: CANADIAN MATHEMATICAL SOCIETY NOTES "It is certainly satisfying for the reader to have almost everything that is known on a particular subject collected in one place. Also, it contributes to a sense of mathematics as a unified subject to see several different areas enter, often in unexpected ways…I can…recommend it to number-theorists and other mathematicians alike; everybody will find useful and interesting information in it. In the classroom, this book might be suitable for undergraduate projects or supplementary readings in a number theory, algebra, or history of mathematics course. It will also be accessible to bright high school students and interested amateurs. In fact, Fermat’s name in the title may attract such readers, and they will find a well written, interesting, and mathematically sound book…"   M. Krizek; F. L. Luca; and L. Somer 17 Lectures on Fermat Numbers From Number Theory to Geometry "The authors have brought together a wealth of material involving the Fermat numbers . . . amateurs and high-school students should also be able to profitably read this well-written book."―MATHEMATICAL REVIEWS "This admirable book contains what must be everything that is worth knowing about Fermat numbers. … It contains a wealth of fascinating results … . The Foreword, by Alena Šolcová, is an excellent account of Fermat’s life and works. … The authors, and the series editors, Jonathan and Peter Borwein, deserve credit and praise for producing what will be the definitive work on the subject for many years to come." (Dudley Underwood, Math DL, May, 2005) "This book was written in celebration of the 400th anniversary of the birth of Pierre de Fermat … . The clear writing style and the evident enthusiasm of the authors make this book a pleasure to read or to dip into. It is not a text book, but might well inspire students at any levels, and it succeeds in making what is potentially a dry and abstract topic fresh and full of connections. It would be a valuable addition to any library." (Alison Wolff, The Australian Mathematical Society Gazette, Vol. 31 (3), 2004) "The book is very interesting and well written – an enjoyable and very thorough collection of all the knowledge on Fermat numbers that have been accumulated during the centuries. … Those who are interested in the history of mathematics will find answers for many questions concerning the history of Fermat numbers. This is an excellent book that can be recommended to all those interested in Fermat numbers or generally in number theory." (László Megyesi, Acta Scientiarium Mathematicarum, Vol. 69, 2003) "In this book the authors have brought together a wealth of material involving the Fermat numbers … . amateurs and high-school students should also be able to profitably read this well-written book. … It has 71 illustrations in total, an extensive list of references and a good subject and name index." (Pieter Moree, Mathematical Reviews, 2002 i) "It is certainly satisfying for the reader to have almost everything that is known on a particular subject collected in one place. … The bibliography, with more than 350 entries, is very complete and contributes to the value of the book as reference, as do the extensive name and subject indexes. … I can … recommend it to number-theorists and other mathematicians alike; everybody will find useful and interesting information in it. … a well written, interesting, and mathematically sound book … ." (CMS Notes, Vol. 34 (8), 2002) "Pierre de Fermat was born just over four h