17 Lectures on Fermat Numbers - Florian Luca

. .

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. The purpose of this book is to provide a general mathematical audience with an overview of Fermat numbers and their numerous appearances and applications in areas such as number theory, probability theory, geometry, and signal processing....

Sommaire:
Foreword by Alena Solcov? * Table of Contents * 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