The fourth edition of Kenneth Rosen's widely used and successful text, Elementary Number Theory and Its Applications, preserves the strengths of the previous editions, while enhancing the book's flexibility and depth of content coverage.
The blending of classical theory with modern applications is a hallmark feature of the text. The Fourth Edition builds on this strength with new examples, additional applications and increased cryptology coverage. Up-to-date information on the latest discoveries is included.
Elementary Number Theory and Its Applications provides a diverse group of exercises, including basic exercises designed to help students develop skills, challenging exercises and computer projects. In addition to years of use and professor feedback, the fourth edition of this text has been thoroughly accuracy checked to ensure the quality of the mathematical content and the exercises
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(美)Kenneth H.Rosen：Kenneth H.Rosen: 1972年获密歇根大学数学学士，1976年获麻省理工学院数学博士学位。曾就职于科罗拉多大学，俄亥俄州立大学，缅因大学，1982年加入AT&T实验室，现为AT&T实验室特别成员，CRC出版社离散数学丛书的主编，是国际知名的计算机数学专家。著有《离散数学及其应用》，《初等数论及其应用》等书。
1. The Integers.
Numbers, Sequences, and Sums.
Mathematical Induction.
The Fibonacci Numbers.
Divisibility.
2. Integer Representation and Operations.
Representation of Integers.
Computer Operations with Integers.
Complexity of Integer Operations.
3. Primes and Greatest Common Divisors.
Prime Numbers.
Greatest Common Divisors.
The Euclidean Algorithm.
The Fundamental Theorem of Arithmetic.
Factorization Methods and the Fermat Numbers.
Linear Diophantine Equations.
4. Congruences.
Introduction to Congruences.
Linear Congruences.
The Chinese Remainder Theorem.
Solving Polynomial Congruences.
Systems of Linear Congruences.
Factoring Using the Pollard rho Method.
5. Applications of Congruences.
Divisibility Tests.
The Perpetual Calendar.
Round-Robin Tournaments.
Hashing Functions.
Check Digits.
6. Some Special Congruences.
Wilson's Theorem and Fermat's Little Theorem.
Pseudoprimes.
Euler's Theorem.
7. Multiplicative Functions.
The Euler Phi-Function.
The Sum and Number of Divisors.
Perfect Numbers and Mersenne Primes.
Möbius Inversion.
8. Cryptology.
Character Ciphers.
Block and Stream Ciphers.
Exponentiation Ciphers.
Public-Key Crytography.
Knapsack Ciphers.
Crytographic Protocols and Applications.
9. Primitive Roots.
The Order of an Integer and Primitive Roots.
Primitive Roots for Primes.
The Existence of Primitive Roots.
Index Arithmetic.
Primality Testing Using Orders of Integers and Primitive Roots.
Universal Exponents.
10. Applications of Primitive Roots and the Order of an Integer.
Pseudorandom Numbers.
The E1Gamal Cryptosystem.
An Application to the Splicing of Telephone Cables.
11. Quadratic Residues.
Quadratic Residues and Nonresidues.
The Law of Quadratic Reciprocity.
The Jacobi Symbol.
Euler Pseudoprimes.
Zero-Knowledge Proofs.
12. Decimal Fractions and Continued Fractions.
Decimal Fractions.
Finite Continued Fractions.
Infinite Continued Fractions.
Periodic Continued Fractions.
Factoring Using Continued Fractions.
13. Some Nonlinear Diophantine Equations.
Pythagorean Triples.
Fermat's Last Theorem.
Sums of Squares.
Pell's Equations.
Appendix A: Axioms for the Set of Integers.
Appendix B: Binomial Coefficients.
Appendix C: Using Maple® and Mathematica for Number Theory.
C.1 Using Maple for Number Theory
C.2 Using Mathematica for Number Theory
Appendix D: Number Theory Web Links.
Appendix E: Tables.
Answers to odd-numbered exercises.
Bibliography.
Index of Biographies.
Index.
