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17 lectures on Fermat numbers : From number theory to geometry

By: Contributor(s): Material type: TextTextLanguage: English Series: CMS books in mathematicsPublication details: New York Springer 2001Description: xxiv, 257p. illISBN:
  • 0387953329 (HB)
Other title:
  • Seventeen lectures on Fermat numbers
Subject(s):
Contents:
* Introduction * Fundamentals of Number Theory * Basic Properties of Fermat Numbers * The Most Beautiful Theorems on Fermat Numbers * Primality of Fermat Numbers * Divisibility of Fermat Numbers * Factors of Fermat Numbers * Connection With the Pascal Triangle * Miscellaneous Results * The Irrationality of the Sum of Some Reciprocals * Fermat Primes and a Diophantine Equation * Fermat's Little Theorem, Pseudoprimes, and Super-Pseudoprimes * Generalizations of Fermat Numbers * Open Problems * Fermat Number Transform and Other Applications * The Proof of Gauss's Theorem * Euclidean Constructions of the Regular Heptadecagon
Summary: 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.
Item type: BOOKS
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IMSc Library 511.52 KRI (Browse shelf(Opens below)) Available 48846

Includes index

Includes bibliography (p. 226-242) references.

* Introduction
* Fundamentals of Number Theory
* Basic Properties of Fermat Numbers
* The Most Beautiful Theorems on Fermat Numbers
* Primality of Fermat Numbers
* Divisibility of Fermat Numbers
* Factors of Fermat Numbers
* Connection With the Pascal Triangle
* Miscellaneous Results
* The Irrationality of the Sum of Some Reciprocals
* Fermat Primes and a Diophantine Equation
* Fermat's Little Theorem, Pseudoprimes, and Super-Pseudoprimes
* Generalizations of Fermat Numbers
* Open Problems
* Fermat Number Transform and Other Applications
* The Proof of Gauss's Theorem
* Euclidean Constructions of the Regular Heptadecagon

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.

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The Institute of Mathematical Sciences, Chennai, India