Elementary Number Theory and Its Applications / Edition 4by Kenneth H. Rosen
Pub. Date: 01/06/2000
This latest edition of Kenneth Rosen's widely used Elementary Number Theory and Its Applications enhances the flexibility and depth of previous editions while preserving their strengths. Rosen effortlessly blends classic theory with contemporary applications. New examples, additional applications and increased cryptology coverage are also included. The book has also been accuracy-checked to ensure the quality of the content. A diverse group of exercises are presented to help develop skills. Also included are computer projects. The book contains updated and increased coverage of Cryptography and new sections on Mvbius Inversion and solving Polynomial Congruences. Historical content has also been enhanced to show the history for the modern material. For those interested in number theory.
- Publication date:
- Edition description:
- Older Edition
- Product dimensions:
- 6.50(w) x 9.00(h) x 1.40(d)
Table of Contents
P. What is Number Theory?
1. The Integers.
Numbers and Sequences.
Sums and Products.
The Fibonacci Numbers.
2. Integer Representations and Operations.
Representations of Integers.
Computer Operations with Integers.
Complexity of Integer Operations.
3. Primes and Greatest Common Divisors.
The Distribution of Primes.
Greatest Common Divisors.
The Euclidean Algorithm.
The Fundemental Theorem of Arithmetic.
Factorization Methods and Fermat Numbers.
Linear Diophantine Equations.
Introduction to Congruences.
The Chinese Remainder Theorem.
Solving Polynomial Congruences.
Systems of Linear Congruences.
Factoring Using the Pollard Rho Method.
5. Applications of Congruences.
The perpetual Calendar.
Round Robin Tournaments.
6. Some Special Congruences.
Wilson's Theorem and Fermat's Little Theorem.
7. Multiplicative Functions.
The Euler Phi-Function.
The Sum and Number of Divisors.
Perfect Numbers and Mersenne Primes.
Block and Stream Ciphers.
Cryptographic Protocols and Applications.
9. Primitive Roots.
The Order of an Integer and Primitive Roots.
Primitive Roots for Primes.
The Existence of Primitive Roots.
Primality Tests Using Orders of Integers and Primitive Roots.
10. Applications of Primitive Roots and the Order of an Integer.
The EIGamal Cryptosystem.
An Application to the Splicing of Telephone Cables.
11. Quadratic Residues.
Quadratic Residues and nonresidues.
The Law of Quadratic Reciprocity.
The Jacobi Symbol.
12. Decimal Fractions and Continued.
Finite Continued Fractions.
Infinite Continued Fractions.
Periodic Continued Fractions.
Factoring Using Continued Fractions.
13. Some Nonlinear Diophantine Equations.
Fermat's Last Theorem.
Sums of Squares.
14. The Gaussian Integers.
Unique Factorization of Gaussian Integers.
Gaussian Integers and Sums of Squares.
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