Elementary Number Theory, 7th edition
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Overview
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.
Published by Pearson (May 24th 2023)  Copyright © 2023
ISBN13: 9780135696897
Subject: Advanced Math
Category: Number Theory
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
 RoundRobin Tournaments
 Hashing Functions
 Check Digits
 Some Special Congruences
 Wilson's Theorem and Fermat's Little Theorem
 Pseudoprimes
 Euler's Theorem
 Arithmetic Functions
 The Euler PhiFunction
 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
 ZeroKnowledge 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
 The Integers
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