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17 Lectures on Fermat Numbers
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From Number Theory to Geometry
Paperback
Print on Demand | Lieferzeit: Print on Demand - Lieferbar innerhalb von 3-5 Werktagen I
Artikel-Nr:
9781441929525
Veröffentl:
2011
Einband:
Paperback
Erscheinungsdatum:
09.10.2011
Seiten:
284
Autor:
Michal Krizek
Gewicht:
435 g
Format:
235x155x16 mm
Serie:
CMS Books in Mathematics
Sprache:
Englisch
Beschreibung:
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. The purpose of this book is to provide a general mathematical audience with an overview of Fermat numbers and their numerous appearances and applications in areas such as number theory, probability theory, geometry, and signal processing.
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.
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.
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.