Undergraduate Texts in Mathematics

Factorization and Primality Testing

Authors: BRESSOUD, DAVID

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About this Textbook

"About binomial theorems I'm teeming with a lot of news, With many cheerful facts about the square on the hypotenuse. " - William S. Gilbert (The Pirates of Penzance, Act I) The question of divisibility is arguably the oldest problem in mathematics. Ancient peoples observed the cycles of nature: the day, the lunar month, and the year, and assumed that each divided evenly into the next. Civilizations as separate as the Egyptians of ten thousand years ago and the Central American Mayans adopted a month of thirty days and a year of twelve months. Even when the inaccuracy of a 360-day year became apparent, they preferred to retain it and add five intercalary days. The number 360 retains its psychological appeal today because it is divisible by many small integers. The technical term for such a number reflects this appeal. It is called a "smooth" number. At the other extreme are those integers with no smaller divisors other than 1, integers which might be called the indivisibles. The mystic qualities of numbers such as 7 and 13 derive in no small part from the fact that they are indivisibles. The ancient Greeks realized that every integer could be written uniquely as a product of indivisibles larger than 1, what we appropriately call prime numbers. To know the decomposition of an integer into a product of primes is to have a complete description of all of its divisors.

Table of contents (14 chapters)

  • Unique Factorization and the Euclidean Algorithm

    Bressoud, David M.

    Pages 1-16

  • Primes and Perfect Numbers

    Bressoud, David M.

    Pages 17-29

  • Fermat, Euler, and Pseudoprimes

    Bressoud, David M.

    Pages 30-42

  • The RSA Public Key Crypto-System

    Bressoud, David M.

    Pages 43-57

  • Factorization Techniques from Fermat to Today

    Bressoud, David M.

    Pages 58-74

Buy this book

eBook n/a
  • ISBN 978-1-4612-4544-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
Hardcover n/a
  • ISBN 978-0-387-97040-0
  • Free shipping for individuals worldwide
Softcover n/a
  • ISBN 978-1-4612-8871-8
  • Free shipping for individuals worldwide
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Bibliographic Information

Bibliographic Information
Book Title
Factorization and Primality Testing
Authors
Series Title
Undergraduate Texts in Mathematics
Copyright
1989
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York, Inc.
eBook ISBN
978-1-4612-4544-5
DOI
10.1007/978-1-4612-4544-5
Hardcover ISBN
978-0-387-97040-0
Softcover ISBN
978-1-4612-8871-8
Series ISSN
0172-6056
Edition Number
1
Number of Pages
XIV, 240
Topics