17 Lectures on Fermat Numbers

From Number Theory to Geometry

Michal Krizek, Florian Luca, Lawrence Somer

258 pages, parution le 28/01/2002

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Résumé

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.

Contents

Foreword

Preface

Glossary of Symbols

Introduction
Fundamentals of Number Theory
Basic Properties of Fermat Numbers
The Most Beautiful Theorems on Fermat Numbers
Primality of Fermat Numbers
Divisibility of Fermat Numbers
Factors of Fermat Numbers
Connection With the Pascal Triangle
Miscellaneous Results
The Irrationality of the Sum of Some Reciprocals
Fermat Primes and a Diophantine Equation
Fermat's Little Theorem, Pseudoprimes, and Super-Pseudoprimes
Generalizations of Fermat Numbers
Open Problems
Fermat Number Transform and Other Applications
The Proof of Gauss's Theorem
Euclidean Constructions of the Regular Heptadecagon

Appendix A, B, C

References

Web Site Sources

Name Index

Subject Index

L'auteur - Michal Krizek

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.

L'auteur - Florian Luca

Florian Luca is a researcher at the Mathematical Institute of the UNAM in Morelia, Mexico.

L'auteur - Lawrence Somer

Lawrence Somer is a Professor of Mathematics at The Catholic University of America in Washington, D. C.

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Michal Krizek, Florian Luca, Lawrence Somer
Parution	28/01/2002
Nb. de pages	258
Format	16 x 24
Couverture	Broché
Poids	524g
Intérieur	Noir et Blanc
EAN13	9780387953328
ISBN13	978-0-387-95332-8