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Primes and Programming Computers and Number Theory

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ISBN-10: 0521409888

ISBN-13: 9780521409889

Edition: 1993

Authors: Peter J. Giblin

List price: $78.99
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Description:

Peter Giblin describes, in the context of an introduction to the theory of numbers, some of the more elementary methods for factorization and primality testing; that is, methods independent of a knowledge of other areas of mathematics. Indeed everything is developed from scratch so the mathematical prerequisites are minimal. An essential feature of the book is the large number of computer programs (written in Pascal) and a wealth of computational exercises and projects, in addition to more usual theory exercises. The theoretical development includes continued fractions and quadratic residues, directed always towards the two fundamental problems of primality testing and factorization. There…    
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Book details

List price: $78.99
Copyright year: 1993
Publisher: Cambridge University Press
Publication date: 9/2/1993
Binding: Paperback
Pages: 252
Size: 6.00" wide x 9.00" long x 0.50" tall
Weight: 0.946
Language: English

Preface
Logical dependence of chapters
The Fundamental Theorem, Greatest Common Divisors and Least Common Multiples
Primes and the fundamental theorem
Greatest common divisor and least common multiple
Euclid's algorithm for the gcd
[x] and applications
Further projects
Listing Primes
Primes by division
Primes by multiplication (elimination of composites)
Approximations to [pi](x)
The sieve of Eratosthenes
Congruences
Congruences: basic properties
Inverses mod m and solutions of certain congruences
Further examples of congruences
Powers and Pseudoprimes
Fermat's (little) theorem
The power algorithm
Head's algorithm for multiplication mod m
Pseudoprimes
Wilson's theorem
Miller's Test and Strong Pseudoprimes
Miller's test
Probabilistic primality testing
Euler's Theorem, Orders and Primality Testing
Euler's function (the [phis]-function or totient function)
Euler's theorem and the concept of order
Primality tests
Periods of decimals
Cryptography
Exponentiation ciphers
Public key cryptography: RSA ciphers
Coin-tossing by telephone
Primitive Roots
Properties and applications of primitive roots
Existence and nonexistence of primitive roots
The Number of Divisors d and the Sum of Divisors [sigma]
The function d(n)
Multiplicative functions and the sum function [sigma](n)
Tests for primality of the Mersenne numbers 2[superscript m] - 1
Continued Fractions and Factoring
Continued fractions: initial ideas and definitions
The continued fraction for [square root]n
Proofs of some properties of continued fractions
Pell's equation
The continued fraction factoring method
Quadratic Residues
Definitions and examples
The quadratic character of 2
Quadratic reciprocity
The Jacobi symbol and a program for finding (n/p)
Solving the equation x[superscript 2] [identical with] a (mod p): quadratic congruences
Bibliography
Index
Index of Listed Programs
Index of Notation