Krizek M., Luca F., Somer L. 17 Lectures on Fermat Numbers: From Number Theory to Geometry

New York: Springer, 2001. — 280 p. — (CMS books in mathematics; 9). — ISBN: 978-1-4419-2952-5, 978-0-387-21850-2.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.ForewordGlossary of SymbolsFundamentals 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 of Fermat Numbers with Pascal's Triangle
Miscellaneous Results
The Irrationality of the Sum of Some Reciprocals
Fermat Primes and a Diophantine Equation
Fermat's Little Theorem, Pseudoprimes, and Superpseudoprimes
Generalizations of Fermat Numbers
Open Problems
Fermat Number Transform and Other Applications
The Proof of Gauss's Theorem
Euclidean Construction of the Regular Heptadecon
Appendix:
Tables of Fermat Numbers and Their Prime Factors
Mersenne Numbers
Remembrance of Pierre de FermatWeb Site Sources
Name Index
Subject Index