David Burton
Elementary Number Theory
https://www.mheducation.com/cover-images/Jpeg_400-high/0073383147.jpeg
Elementary Number Theory
7th Edition
By David Burton
ISBN10: 0073383147
ISBN13: 9780073383149
Copyright: 2011
ISBN10: 0073383147
ISBN13: 9780073383149
Copyright: 2011
Product Details +
Elementary Number Theory, Seventh Edition, is written for the one-semester undergraduate number theory course taken by math majors, secondary education majors, and computer science students. This contemporary text provides a simple account of classical number theory, set against a historical background that shows the subject's evolution from antiquity to recent research.
Read more +
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
Orders within the United States are shipped via Fedex or UPS Ground.
For shipments to locations outside of the U.S., only standard shipping is available.
All shipping options assumes the product is available and that it will take 24 to 48 hours to process your order prior to shipping.
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.