Elementary Number Theory and Its Applications

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 Historical content has also been enhanced to show the history for the modern material.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. Preface Contents Introduction 1. The Integers The well-ordering property Divisibility Representation of integers Computer operations with integers Prime numbers 2. Greatest Common Divisors and Prime Factorization Greatest common divisors The Euclidean algorithm The fundamental theorem of arithmetic Factorization of integers and the Fermat numbers Linear diophantine equations 3. Congruences Introduction to congruences Linear congruences The Chinese remainder theorem Systems of linear congruences 4. Applications of Congruences Divisibility tests The perpetual calendar Round-robin tournaments Computer file storage and hashing functions 5. Some Special Congruences Wilson's theorem and Fermat's little theorem Pseudoprimes Euler's theorem 6. Multiplicative Functions Euler's phi-function The sum and number of divisors Perfect numbers and Mersenne primes 7. Cryptology Character ciphers Block ciphers Exponentiation ciphers Public-key cryptography Knapsack ciphers Some applications to computer science 8. Primitive Roots The order of an integer and primitive roots Primitive roots for primes Existence of primitive roots Index arithmetic Primality testing using primitive roots Universal exponents Psuedo-random numbers The splicing of telephone cables 9. Quadratic Residues and Reciprocity Quadratic residues Quadratic reciprocity The Jacobi symbol Euler pseudoprimes 10. Decimal Fractions and Continued Fractions Decimal fractions Finite continued fractions Infinite continued fractions Periodic continued fractions 11. Some Nonlinear Diophantine Equations Pythagorean triples Fermat's last theorem Pell's equations Appendix Answers to selected problems Bibliography List of symbols Index Kenneth H. Rosen. Includes Index. Bibliography: P. 438-444.