# Elementary Number Theory

7^{th}Edition

ISBN10: 0073383147

ISBN13: 9780073383149

Copyright: 2011

Instructors:

Get your free copy today

Sign-in to get your free copy or create a new account

Considering using this product for your course? Request a free copy to evaluate if it'll be the best resource for you. You can get a free copy of any textbook to review.

**Review the content, imagery, and approach**- make sure it's the best resource for you**There's no cost to you**- just needs to be approved by your McGraw-Hill Learning Technology Rep**No account yet, no problem**- just register on the next step and you'll be assigned a personal Learning Technology Rep who can send you your copy

Still Have Questions?

Contact a Tech Rep
s

## Purchase Options

Students, we’re committed to providing you with high-value course solutions backed by great service and a team that cares about your success. See tabs below to explore options and prices.

### Hardcopy

Out of stock

Receive via shipping:

- Bound book containing the complete text
- Full color
- Hardcover or softcover

Purchase

$165.48

The estimated amount of time this product will be on the market is based on a number of factors, including faculty input to instructional design and the prior revision cycle and updates to academic research-which typically results in a revision cycle ranging from every two to four years for this product. Pricing subject to change at any time.

The estimated amount of time this product will be on the market is based on a number of factors, including faculty input to instructional design and the prior revision cycle and updates to academic research-which typically results in a revision cycle ranging from every two to four years for this product. Pricing subject to change at any time.

### Program Details

# Elementary Number Theory, 7e, by David M. Burton

# Table of Contents

## Preface

## New to this Edition

## 1 Preliminaries

#### 1.1 Mathematical Induction

#### 1.2 The Binomial Theorem

## 2 Divisibility Theory in the Integers

#### 2.1 Early Number Theory

#### 2.2 The Division Algorithm

#### 2.3 The Greatest Common Divisor

#### 2.4 The Euclidean Algorithm

#### 2.5 The Diophantine Equation

## 3 Primes and Their Distribution

#### 3.1 The Fundamental Theorem of Arithmetic

#### 3.2 The Sieve of Eratosthenes

#### 3.3 The Goldbach Conjecture

## 4 The Theory of Congruences

#### 4.1 Carl Friedrich Gauss

#### 4.2 Basic Properties of Congruence

#### 4.3 Binary and Decimal Representations of Integers

#### 4.4 Linear Congruences and the Chinese Remainder Theorem

## 5 Fermat’s Theorem

#### 5.1 Pierre de Fermat

#### 5.2 Fermat’s Little Theorem and Pseudoprimes

#### 5.3 Wilson’s Theorem

#### 5.4 The Fermat-Kraitchik Factorization Method

## 6 Number-Theoretic Functions

#### 6.1 The Sum and Number of Divisors

#### 6.2 The Möbius Inversion Formula

#### 6.3 The Greatest Integer Function

#### 6.4 An Application to the Calendar

## 7 Euler’s Generalization of Fermat’s Theorem

#### 7.1 Leonhard Euler

#### 7.2 Euler’s Phi-Function

#### 7.3 Euler’s Theorem

#### 7.4 Some Properties of the Phi-Function

## 8 Primitive Roots and Indices

#### 8.1 The Order of an Integer Modulo n

#### 8.2 Primitive Roots for Primes

#### 8.3 Composite Numbers Having Primitive Roots

#### 8.4 The Theory of Indices

## 9 The Quadratic Reciprocity Law

#### 9.1 Euler’s Criterion

#### 9.2 The Legendre Symbol and Its Properties

#### 9.3 Quadratic Reciprocity

#### 9.4 Quadratic Congruences with Composite Moduli

## 10 Introduction to Cryptography

#### 10.1 From Caesar Cipher to Public Key Cryptography

#### 10.2 The Knapsack Cryptosystem

#### 10.3 An Application of Primitive Roots to Cryptography

## 11 Numbers of Special Form

#### 11.1 Marin Mersenne

#### 11.2 Perfect Numbers

#### 11.3 Mersenne Primes and Amicable Numbers

#### 11.4 Fermat Numbers

## 12 Certain Nonlinear Diophantine Equations

#### 12.1 The Equation

#### 12.2 Fermat’s Last Theorem

## 13 Representation of Integers as Sums of Squares

#### 13.1 Joseph Louis Lagrange

#### 13.2 Sums of Two Squares

#### 13.3 Sums of More Than Two Squares

## 14 Fibonacci Numbers

#### 14.1 Fibonacci

#### 14.2 The Fibonacci Sequence

#### 14.3 Certain Identities Involving Fibonacci Numbers

## 15 Continued Fractions

#### 15.1 Srinivasa Ramanujan

#### 15.2 Finite Continued Fractions

#### 15.3 Infinite Continued Fractions

#### 15.4 Farey Fractions

#### 15.5 Pell’s Equation

## 16 Some Recent Developments

#### 16.1 Hardy, Dickson, and Erdös

#### 16.2 Primality Testing and Factorization

#### 16.3 An Application to Factoring: Remote Coin Flipping

#### 16.4 The Prime Number Theorem and Zeta Function

## Miscellaneous Problems

## Appendixes

## General References

## Suggested Further Reading

## Tables

## Answers to Selected Problems

## Index

# Elementary Number Theory, 7e, by David M. Burton

# Table of Contents

## Preface

## New to this Edition

## 1 Preliminaries

#### 1.1 Mathematical Induction

#### 1.2 The Binomial Theorem

## 2 Divisibility Theory in the Integers

#### 2.1 Early Number Theory

#### 2.2 The Division Algorithm

#### 2.3 The Greatest Common Divisor

#### 2.4 The Euclidean Algorithm

#### 2.5 The Diophantine Equation

## 3 Primes and Their Distribution

#### 3.1 The Fundamental Theorem of Arithmetic

#### 3.2 The Sieve of Eratosthenes

#### 3.3 The Goldbach Conjecture

## 4 The Theory of Congruences

#### 4.1 Carl Friedrich Gauss

#### 4.2 Basic Properties of Congruence

#### 4.3 Binary and Decimal Representations of Integers

#### 4.4 Linear Congruences and the Chinese Remainder Theorem

## 5 Fermat’s Theorem

#### 5.1 Pierre de Fermat

#### 5.2 Fermat’s Little Theorem and Pseudoprimes

#### 5.3 Wilson’s Theorem

#### 5.4 The Fermat-Kraitchik Factorization Method

## 6 Number-Theoretic Functions

#### 6.1 The Sum and Number of Divisors

#### 6.2 The Möbius Inversion Formula

#### 6.3 The Greatest Integer Function

#### 6.4 An Application to the Calendar

## 7 Euler’s Generalization of Fermat’s Theorem

#### 7.1 Leonhard Euler

#### 7.2 Euler’s Phi-Function

#### 7.3 Euler’s Theorem

#### 7.4 Some Properties of the Phi-Function

## 8 Primitive Roots and Indices

#### 8.1 The Order of an Integer Modulo n

#### 8.2 Primitive Roots for Primes

#### 8.3 Composite Numbers Having Primitive Roots

#### 8.4 The Theory of Indices

## 9 The Quadratic Reciprocity Law

#### 9.1 Euler’s Criterion

#### 9.2 The Legendre Symbol and Its Properties

#### 9.3 Quadratic Reciprocity

#### 9.4 Quadratic Congruences with Composite Moduli

## 10 Introduction to Cryptography

#### 10.1 From Caesar Cipher to Public Key Cryptography

#### 10.2 The Knapsack Cryptosystem

#### 10.3 An Application of Primitive Roots to Cryptography

## 11 Numbers of Special Form

#### 11.1 Marin Mersenne

#### 11.2 Perfect Numbers

#### 11.3 Mersenne Primes and Amicable Numbers

#### 11.4 Fermat Numbers

## 12 Certain Nonlinear Diophantine Equations

#### 12.1 The Equation

#### 12.2 Fermat’s Last Theorem

## 13 Representation of Integers as Sums of Squares

#### 13.1 Joseph Louis Lagrange

#### 13.2 Sums of Two Squares

#### 13.3 Sums of More Than Two Squares

## 14 Fibonacci Numbers

#### 14.1 Fibonacci

#### 14.2 The Fibonacci Sequence

#### 14.3 Certain Identities Involving Fibonacci Numbers

## 15 Continued Fractions

#### 15.1 Srinivasa Ramanujan

#### 15.2 Finite Continued Fractions

#### 15.3 Infinite Continued Fractions

#### 15.4 Farey Fractions

#### 15.5 Pell’s Equation

## 16 Some Recent Developments

#### 16.1 Hardy, Dickson, and Erdös

#### 16.2 Primality Testing and Factorization

#### 16.3 An Application to Factoring: Remote Coin Flipping

#### 16.4 The Prime Number Theorem and Zeta Function

## Miscellaneous Problems

## Appendixes

## General References

## Suggested Further Reading

## Tables

## Answers to Selected Problems

## Index

#### Shipping Options

- Standard
- Next day air
- 2nd day air
- 3rd day air

#### Rent Now

You will be taken to our partner Chegg.com to complete your transaction.

After completing your transaction, you can access your course using the section url supplied by your instructor.