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Primes and programming : an introduction to number theory with computing

Author: P J Giblin
Publisher: Cambridge [England] ; New York : Cambridge University Press, 1993.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: P J Giblin
ISBN: 0521401828 9780521401821 0521409888 9780521409889
OCLC Number: 28910962
Description: x, 235 p. : ill. ; 24 cm.
Contents: 1. The Fundamental Theorem, Greatest Common Divisors and Least Common Multiples. 1. Primes and the fundamental theorem. 2. Greatest common divisor and least common multiple. 3. Euclid's algorithm for the gcd. 4. [x] and applications. 5. Further projects --
2. Listing Primes. 1. Primes by division. 2. Primes by multiplication (elimination of composites). 3. Approximations to [pi](x). 4. The sieve of Eratosthenes --
3. Congruences. 1. Congruences: basic properties. 2. Inverses mod m and solutions of certain congruences. 3. Further examples of congruences --
4. Powers and Pseudoprimes. 1. Fermat's (little) theorem. 2. The power algorithm. 3. Head's algorithm for multiplication mod m. 4. Pseudoprimes. 5. Wilson's theorem --
5. Miller's Test and Strong Pseudoprimes. 1. Miller's test. 2. Probabilistic primality testing --
6. Euler's Theorem, Orders and Primality Testing. 1. Euler's function (the [phi] function or totient function). 2. Euler's theorem and the concept of order. 3. Primality tests. 4. Periods of decimals --
7. Cryptography. 1. Exponentiation ciphers. 2. Public key cryptography: RSA ciphers. 3. Coin-tossing by telephone --
8. Primitive Roots. 1. Properties and applications of primitive roots. 2. Existence and nonexistence of primitive roots --
9. The Number of Divisors d and the Sum of Divisors [sigma]. 1. The function d(n). 2. Multiplicative functions and the sum function [sigma](n). 3. Tests for primality of the Mersenne numbers 2[superscript m] --
1 --
10. Continued Fractions and Factoring. 1. Continued fractions: initial ideas and definitions. 2. The continued fraction for [actual symbol not reproducible]n. 3. Proofs of some properties of continued fractions. 4. Pell's equation. 5. The continued fraction factoring method --
11. Quadratic Residues. 1. Definitions and examples. 2. The quadratic character of 2. 3. Quadratic reciprocity. 4. The Jacobi symbol and a program for finding [actual symbol not reproducible]. 5. Solving the equation x[superscript 2] [actual symbol not reproducible] a (mod p): quadratic congruences.
Responsibility: Peter Giblin.
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