17 Lectures on Fermat Numbers

From Number Theory to Geometry
2002. Auflage 2002
ISBN: 978-0-387-95332-8
Verlag: Springer

Buch, Englisch, 257 Seiten, Format (B × H): 162 mm x 245 mm, Gewicht: 526 g

Reihe: CMS Books in Mathematics

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.

Zielgruppe

Popular/general

Autoren/Hrsg.

Krizek, Michal

Luca, Florian

Somer, Lawrence

Weitere Mitwirkende

Solcova, A.

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Zahlentheorie
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Interdisziplinäres Wissenschaften Wissenschaften: Allgemeines Geschichte der Naturwissenschaften, Formalen Wissenschaften & Technik
• Mathematik | Informatik Mathematik Mathematik Allgemein Geschichte der Mathematik

Inhaltsverzeichnis

1. Introduction.- 2. Fundamentals of Number Theory.- 3. Basic Properties of Fermat Numbers.- 4. The Most Beautiful Theorems on Fermat Numbers.- 5. Primality of Fermat Numbers.- 6. Divisibility of Fermat Numbers.- 7. Factors of Fermat Numbers.- 8. Connection of Fermat Numbers with Pascal’s Triangle.- 9. Miscellaneous Results.- 10. The Irrationality of the Sum of Some Reciprocals.- 11. Fermat Primes and a Diophantine Equation.- 12. Fermat’s Little Theorem, Pseudoprimes, and Superpseudoprimes.- 13. Generalizations of Fermat Numbers.- 14. Open Problems.- 15. Fermat Number Transform and Other Applications.- 16. The Proof of Gauss’s Theorem.- 17. Euclidean Construction of the Regular Heptadecagon.- A. Tables of Fermat Numbers and Their Prime Factors.- B. Mersenne Numbers.- C. Remembrance of Pierre de Fermat.- References.- Web Site Sources.- Name Index.