17 lectures on fermat numbers論費(fèi)馬數(shù)的17篇文獻(xiàn)

內(nèi)容概要

The pioneering work of French mathematician Pierre de Fermat has attracted the attention of mathematicians for over 350 years. This book was written in honor of the 400th anniversary of his birth, providing readers with an overview of the many properties of Fermat numbers and demonstrating their 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.

書(shū)籍目錄

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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