17 Lectures on Fermat Numbers From Number Theory to Geometry
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 bir...
| Main Authors: | , , |
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| Format: | eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
2001, 2001
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| Edition: | 1st ed. 2001 |
| Series: | CMS Books in Mathematics, Ouvrages de mathématiques de la SMC
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 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