☀️ SUMMER SALE! 40% off your first month of eTextbooks. Use code SUMMER40. Terms & Conditions

Secure Checkout

Elementary Number Theory, 7th edition

  • Kenneth H. Rosen

Your access includes:

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

$10.99per month

Minimum 4-month term, pay monthly or pay $43.96 upfront

Looking for your MyLab or Mastering eTextbook? Find it hereOpens in an new tab

Learn more, spend less

  • 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

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

ISBN-13: 9780135696897

Subject: Advanced Math

Category: Number Theory

Overview

    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 1-stop shop with eTextbooks, study tools and exam prep features designed to help students get better grades in college. eTextbooks come with built-in tools that simplify studying, like flashcards, audiobook and search. Pearson+ also features Channels, which includes practice problems, study guides, Q&A with experts, video lessons that help you understand tricky topics and more—all in one place. Channels can be purchased separately or added on to your eTextbook at the time of purchase as part of the Study & Exam Prep Pack.

A Pearson eTextbook is an easy-to-use digital version of your book for class that includes upgraded study tools to help you learn how you learn best. Use enhanced search to find what you need within your eTextbook, highlight and make notes to mark important info, generate flashcards to test your knowledge, and use audio to listen to the text. Every feature is designed to help you learn more efficiently and get results. Plus, you can learn on the go with the Pearson+ app. Find this and more in your eTextbook, available in Pearson+.

The Study & Exam Prep Pack includes practice problems, study guides, Q&A with experts, Channels video lessons that help you understand tricky topics and more. It can be added on to your eTextbook or your MyLab and Mastering learning platform at the time of purchase.

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.