Elementary Number Theory, 7th edition

  • Kenneth H. Rosen

Your access includes:

  • Search, highlight, and take notes
  • Easily create flashcards
  • Use the app for access anywhere
  • 14-day refund guarantee

$10.99per month

4-month term, pay monthly or pay $43.96

Learn more, spend less

  • Special partners and offers

    Enjoy perks from special partners and offers for students

  • Find it fast

    Quickly navigate your eTextbook with search

  • Stay organized

    Access all your eTextbooks in one place

  • Easily continue access

    Keep learning with auto-renew


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

ISBN-13: 9780135696897

Subject: Advanced Math

Category: Number Theory

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

Your questions answered

Pearson+ is your one-stop shop, with eTextbooks and study videos designed to help students get better grades in college.

A Pearson eTextbook is an easy‑to‑use digital version of the book. You'll get upgraded study tools, including enhanced search, highlights and notes, flashcards and audio. Plus learn on the go with the Pearson+ app.

Your eTextbook subscription gives you access for 4 months. You can make a one‑time payment for the initial 4‑month term or pay monthly. If you opt for monthly payments, we will charge your payment method each month until your 4‑month term ends. You can turn on auto‑renew in My account at any time to continue your subscription before your 4‑month term ends.

When you purchase an eTextbook subscription, it will last 4 months. You can renew your subscription by selecting Extend subscription on the Manage subscription page in My account before your initial term ends.

If you extend your subscription, we'll automatically charge you every month. If you made a one‑time payment for your initial 4‑month term, you'll now pay monthly. To make sure your learning is uninterrupted, please check your card details.

To avoid the next payment charge, select Cancel subscription on the Manage subscription page in My account before the renewal date. You can subscribe again in the future by purchasing another eTextbook subscription.

Channels is a video platform with thousands of explanations, solutions and practice problems to help you do homework and prep for exams. Videos are personalized to your course, and tutors walk you through solutions. Plus, interactive AI‑powered summaries and a social community help you better understand lessons from class.

Channels is an additional tool to help you with your studies. This means you can use Channels even if your course uses a non‑Pearson textbook.

When you choose a Channels subscription, you're signing up for a 1‑month, 3‑month or 12‑month term and you make an upfront payment for your subscription. By default, these subscriptions auto‑renew at the frequency you select during checkout.

When you purchase a Channels subscription it will last 1 month, 3 months or 12 months, depending on the plan you chose. Your subscription will automatically renew at the end of your term unless you cancel it.

We use your credit card to renew your subscription automatically. To make sure your learning is uninterrupted, please check your card details.