Author | Kลรญลพek, Michal. author |
---|---|
Title | 17 Lectures on Fermat Numbers [electronic resource] : From Number Theory to Geometry / by Michal Kลรญลพek, Florian Luca, Lawrence Somer |
Imprint | New York, NY : Springer New York : Imprint: Springer, 2001 |
Connect to | http://dx.doi.org/10.1007/978-0-387-21850-2 |
Descript | XXIV, 257 p. online resource |
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 Pascalโs Triangle -- 9. Miscellaneous Results -- 10. The Irrationality of the Sum of Some Reciprocals -- 11. Fermat Primes and a Diophantine Equation -- 12. Fermatโs Little Theorem, Pseudoprimes, and Superpseudoprimes -- 13. Generalizations of Fermat Numbers -- 14. Open Problems -- 15. Fermat Number Transform and Other Applications -- 16. The Proof of Gaussโs 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