17 Lectures on Fermat Numbers
From Number Theory to Geometry
Authors: Krizek, Michal, Luca, Florian, Somer, Lawrence
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 About this book

French mathematician Pierre de Fermat became most well known for his pioneering work in the area of number theory. His work with numbers has been attracting the attention of amateur and professional mathematicians for over 350 years. This book was written in honor of the 400th anniversary of his birth and is based on a series of lectures given by the authors. The purpose of this book is to provide readers with an overview of the many properties of Fermat numbers and to demonstrate their numerous appearances and applications in areas such as number theory, probability theory, geometry, and signal processing. This book introduces a general mathematical audience to basic mathematical ideas and algebraic methods connected with the Fermat numbers and will provide invaluable reading for the amateur and professional alike.
Michal Krizek is a senior researcher at the Mathematical Institute of the Academy of Sciences of the Czech Republic and Associate Professor in the Department of Mathematics and Physics at Charles University in Prague. Florian Luca is a researcher at the Mathematical Institute of the UNAM in Morelia, Mexico. Lawrence Somer is a Professor of Mathematics at The Catholic University of America in Washington, D. C.  Reviews

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 numbertheorists 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 highschool students should also be able to profitably read this wellwritten 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 400^{th} 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 highschool students should also be able to profitably read this wellwritten 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 numbertheorists 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 hundred years ago, and this book is in part a celebration of his quatercentenary. … A pleasing feature of the exposition is that as many results as possible are illustrated pictorially. … The text is copiously illustrated with both photographs and excellent diagrams, and I can recommend the book as a whole to anyone who wants to venture into this treasuretrove of somewhat arcane number theory." (Gerry Leversha, The Mathematical Gazette, Vol. 87 (509), 2003)
"The purpose of this book is to provide readers with an overview of the many properties of Fermat numbers and to demonstrate their numerous appearances and applications … . This book introduces a general mathematical audience to basic mathematical ideas and algebraic methods connected with the Fermat numbers and provides invaluable reading for amateurs and professionals alike." (L’Enseignement Mathématique, Vol. 48 (12), 2002)
 Table of contents (17 chapters)


Introduction
Pages 18

Fundamentals of Number Theory
Pages 925

Basic Properties of Fermat Numbers
Pages 2632

The Most Beautiful Theorems on Fermat Numbers
Pages 3340

Primality of Fermat Numbers
Pages 4158

Table of contents (17 chapters)
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Bibliographic Information
 Bibliographic Information

 Book Title
 17 Lectures on Fermat Numbers
 Book Subtitle
 From Number Theory to Geometry
 Authors

 Michal Krizek
 Florian Luca
 Lawrence Somer
 Series Title
 CMS Books in Mathematics
 Copyright
 2001
 Publisher
 SpringerVerlag New York
 Copyright Holder
 SpringerVerlag New York
 eBook ISBN
 9780387218502
 DOI
 10.1007/9780387218502
 Hardcover ISBN
 9780387953328
 Softcover ISBN
 9781441929525
 Series ISSN
 16135237
 Edition Number
 1
 Number of Pages
 XXIV, 257
 Topics