Pearson eText -- Elementary Number Theory -- Access Card

Elementary Number Theory helps you push your understanding to new heights with the strongest exercise sets, proofs and examples. Applications are integrated throughout. Connections with abstract algebra help those who have already studied it, and lay the groundwork to understand key ideas if you're taking abstract algebra in the future.  Computational exercises and computer projects are available  for  Maple,  Mathematica, Sage Math and the  book's  many  online resources.  The 7th Edition offers a presentation that's easier to learn from,  while incorporating advancements and  recent  discoveries in  number theory.  Expanded coverage of cryptography includes elliptic curve photography; the important notion of homomorphic encryption is introduced, and coverage of knapsack ciphers has been removed. Several  hundred  new exercises enhance the text's exercise sets.

Table of Contents:
The Integers Numbers and Sequences Diophantine Approximation Sums and Products Mathematical Induction The Fibonacci Numbers Divisibility Integer Representations and Operations Representations of Integers Computer Operations with Integers Complexity of Integer Operations Greatest Common Divisors Greatest Common Divisors and Their Properties The Euclidean Algorithm Linear Diophantine Equations Prime Numbers Prime Numbers The Distribution of Primes The Fundamental Theorem of Arithmetic Factorization Methods and the Fermat Numbers Congruences Introduction to Congruences Linear Congruences The Chinese Remainder Theorem Polynomial Congruences Systems of Linear Congruences Applications of Congruences Divisibility Tests The Perpetual Calendar Round-Robin Tournaments Hashing Functions Check Digits Some Special Congruences Wilson's Theorem and Fermat's Little Theorem Pseudoprimes Euler's Theorem Arithmetic Functions The Euler Phi-Function The Sum and Number of Divisors Perfect Numbers and Mersenne Primes Möbius Inversion Partitions Cryptography Character Ciphers Block and Stream Ciphers Exponentiation Ciphers Public Key Cryptography Cryptographic Protocols and Applications Primitive Roots The Order of an Integer and Primitive Roots Primitive Roots for Primes The Existence of Primitive Roots Discrete Logarithms and Index Arithmetic Primality Tests Using Orders of Integers and Primitive Roots Universal Exponents Applications of Primitive Roots and the Order of an Integer Pseudorandom Numbers The EIGamal Cryptosystem An Application to the Splicing of Telephone Cables Quadratic Residues Quadratic Residues and Nonresidues The Law of Quadratic Reciprocity The Jacobi Symbol Euler Pseudoprimes Zero-Knowledge Proofs Decimal Fractions and Continued Fractions Decimal Fractions Finite Continued Fractions Infinite Continued Fractions Periodic Continued Fractions Factoring Using Continued Fractions Nonlinear Diophantine Equations and Elliptic Curves Pythagorean Triples Fermat's Last Theorem Sum of Squares Pell's Equation Congruent Numbers and Elliptic Curves Elliptic Curves Modulo Primes Applications of Elliptic Curves The Gaussian Integers Gaussian Integers and Gaussian Primes Greatest Common Divisors and Unique Factorization Gaussian Integers and Sums of Squares

About the Author :
About our author Kenneth H. Rosen received his BS in mathematics from the University of Michigan - Ann Arbor (1972) and his PhD in mathematics from MIT (1976). Before joining Bell Laboratories in 1982, he held positions at the University of Colorado - Boulder, The Ohio State University - Columbus, and the University of Maine - Orono, where he was an associate professor of mathematics. While working at AT&T Laboratories, he taught at Monmouth University, teaching courses in discrete mathematics, coding theory, and data security.  Dr. Rosen has published numerous articles in professional journals in the areas of number theory and mathematical modeling. He is the author of Elementary Number Theory,  7th Edition and other books.