17 lectures on fermat numbers论费马数的17篇文献

作者简介

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.

书籍目录

ForewordPrefaceGlossary of Symbols1. Introduction2. Fundamentals of Number Theory3. Basic Properties of Fermat Numbers4. The Most Beautiful Theorems on Fermat Numbers5. Primality of Fermat Numbers6. Divisibility of Fermat Numbers7. Factors of Fermat Numbers8. Connection of Fermat Numbers with Pascal's Triangle9. Miscellaneous Results10. The Irrationality of the Sum of Some Reciprocals11. Fermat Primes and a Diophantine Equation12. Fermat's Little Theorem, Pseudoprimes, and Superpseudoprimes13. Generalizations of Fermat Numbers14. Open Problems15. Fermat Number Transform and Other Applications16. The Proof of Gauss's Theorem17. Euclidean Construction of the Regular Heptadecagon　　Appendix　　　A. Tables of Fermat Numbers and Their Prime Factors      B. Mersenne Numbers      C. Remembrance of Pierre de Fermat　　References　　Web Site Sources     Name Index    Subject Index

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