17 Lectures on Fermat Numbers

From Number Theory to Geometry

Authors:

ISBN: 978-1-4419-2952-5 (Print) 978-0-387-21850-2 (Online)

Table of contents (17 chapters)

  1. Front Matter

    Pages i-xxiv

  2. No Access

    Book Chapter

    Pages 1-8

    Introduction

  3. No Access

    Book Chapter

    Pages 9-25

    Fundamentals of Number Theory

  4. No Access

    Book Chapter

    Pages 26-32

    Basic Properties of Fermat Numbers

  5. No Access

    Book Chapter

    Pages 33-40

    The Most Beautiful Theorems on Fermat Numbers

  6. No Access

    Book Chapter

    Pages 41-58

    Primality of Fermat Numbers

  7. No Access

    Book Chapter

    Pages 59-69

    Divisibility of Fermat Numbers

  8. No Access

    Book Chapter

    Pages 70-79

    Factors of Fermat Numbers

  9. No Access

    Book Chapter

    Pages 80-93

    Connections of Fermat Numbers with Pascal’s Triangle

  10. No Access

    Book Chapter

    Pages 94-103

    Miscellaneous Results

  11. No Access

    Book Chapter

    Pages 104-116

    The Irrationality of the Sum of Some Reciprocals

  12. No Access

    Book Chapter

    Pages 117-129

    Fermat Primes and a Diophantine Equation

  13. No Access

    Book Chapter

    Pages 130-146

    Fermat’s Little Theorem, Pseudoprimes, and Superpseudoprimes

  14. No Access

    Book Chapter

    Pages 147-157

    Generalizations of Fermat Numbers

  15. No Access

    Book Chapter

    Pages 158-164

    Open Problems

  16. No Access

    Book Chapter

    Pages 165-186

    Fermat Number Transform and Other Applications

  17. No Access

    Book Chapter

    Pages 187-192

    The Proof of Gauss’s Theorem

  18. No Access

    Book Chapter

    Pages 193-206

    Euclidean Construction of the Regular Heptadecagon

  19. Back Matter

    Pages 207-257