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© 2001

17 Lectures on Fermat Numbers

From Number Theory to Geometry

Book

Table of contents

  1. Front Matter
    Pages i-xxiv
  2. Michal Křížek, Florian Luca, Lawrence Somer
    Pages 1-8
  3. Michal Křížek, Florian Luca, Lawrence Somer
    Pages 9-25
  4. Michal Křížek, Florian Luca, Lawrence Somer
    Pages 26-32
  5. Michal Křížek, Florian Luca, Lawrence Somer
    Pages 33-40
  6. Michal Křížek, Florian Luca, Lawrence Somer
    Pages 41-58
  7. Michal Křížek, Florian Luca, Lawrence Somer
    Pages 59-69
  8. Michal Křížek, Florian Luca, Lawrence Somer
    Pages 70-79
  9. Michal Křížek, Florian Luca, Lawrence Somer
    Pages 80-93
  10. Michal Křížek, Florian Luca, Lawrence Somer
    Pages 94-103
  11. Michal Křížek, Florian Luca, Lawrence Somer
    Pages 104-116
  12. Michal Křížek, Florian Luca, Lawrence Somer
    Pages 117-129
  13. Michal Křížek, Florian Luca, Lawrence Somer
    Pages 130-146
  14. Michal Křížek, Florian Luca, Lawrence Somer
    Pages 147-157
  15. Michal Křížek, Florian Luca, Lawrence Somer
    Pages 158-164
  16. Michal Křížek, Florian Luca, Lawrence Somer
    Pages 165-186
  17. Michal Křížek, Florian Luca, Lawrence Somer
    Pages 187-192
  18. Michal Křížek, Florian Luca, Lawrence Somer
    Pages 193-206
  19. Back Matter
    Pages 207-257

About this book

Introduction

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.

Keywords

Fermat Fermat Numbers History of Mathematics Mersenne number Prime number theory

Authors and affiliations

  1. 1.Mathematical InstituteAcademy of SciencesCzech Republic
  2. 2.Mathematical InstituteNational Autonomous University of MexicoMoreliaMexico
  3. 3.Department of MathematicsCatholic University of AmericaUSA

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 / Ouvrages de mathématiques de la SMC
  • DOI https://doi.org/10.1007/978-0-387-21850-2
  • Copyright Information Springer-Verlag New York 2001
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-387-95332-8
  • Softcover ISBN 978-1-4419-2952-5
  • eBook ISBN 978-0-387-21850-2
  • Series ISSN 1613-5237
  • Edition Number 1
  • Number of Pages XXIV, 257
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Number Theory
    History of Mathematical Sciences
    Geometry
  • Buy this book on publisher's site
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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 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 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 treasure-trove 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 (1-2), 2002)