Elementary Number Theory, 7th edition

Published by Pearson (24 May 2023) © 2024

  • Kenneth H. Rosen AT&T Laboratories

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ISBN-13: 9780321974334
Elementary Number Theory
Published 2022

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Table of contents

    1. The Integers
      • Numbers and Sequences
      • Diophantine Approximation
      • Sums and Products
      • Mathematical Induction
      • The Fibonacci Numbers
      • Divisibility
    2. Integer Representations and Operations
      • Representations of Integers
      • Computer Operations with Integers
      • Complexity of Integer Operations
    3. Greatest Common Divisors
      • Greatest Common Divisors and Their Properties
      • The Euclidean Algorithm
      • Linear Diophantine Equations
    4. Prime Numbers
      • Prime Numbers
      • The Distribution of Primes
      • The Fundamental Theorem of Arithmetic
      • Factorization Methods and the Fermat Numbers
    5. Congruences
      • Introduction to Congruences
      • Linear Congruences
      • The Chinese Remainder Theorem
      • Polynomial Congruences
      • Systems of Linear Congruences
    6. Applications of Congruences
      • Divisibility Tests
      • The Perpetual Calendar
      • Round-Robin Tournaments
      • Hashing Functions
      • Check Digits
    7. Some Special Congruences
      • Wilson's Theorem and Fermat's Little Theorem
      • Pseudoprimes
      • Euler's Theorem
    8. Arithmetic Functions
      • The Euler Phi-Function
      • The Sum and Number of Divisors
      • Perfect Numbers and Mersenne Primes
      • Möbius Inversion
      • Partitions
    9. Cryptography
      • Character Ciphers
      • Block and Stream Ciphers
      • Exponentiation Ciphers
      • Public Key Cryptography
      • Cryptographic Protocols and Applications
    10. 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
    11. Applications of Primitive Roots and the Order of an Integer
      • Pseudorandom Numbers
      • The EIGamal Cryptosystem
      • An Application to the Splicing of Telephone Cables
    12. Quadratic Residues
      • Quadratic Residues and Nonresidues
      • The Law of Quadratic Reciprocity
      • The Jacobi Symbol
      • Euler Pseudoprimes
      • Zero-Knowledge Proofs
    13. Decimal Fractions and Continued Fractions
      • Decimal Fractions
      • Finite Continued Fractions
      • Infinite Continued Fractions
      • Periodic Continued Fractions
      • Factoring Using Continued Fractions
    14. 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
    15. The Gaussian Integers
      • Gaussian Integers and Gaussian Primes
      • Greatest Common Divisors and Unique Factorization
      • Gaussian Integers and Sums of Squares

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