Elementary Number Theory, 7th Edition David Burton

 Elementary Number Theory,

7th Edition

ISBN: 9780073383149 / 0073383147 

Author: David Burton

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Chapter 1

Preliminaries

1-1	Mathematical Induction
1-2	The Binomial Theorem

Chapter 2

Divisibility Theory In The Integers

	Early Number  Theory
	The Division Algorithm
	The Greatest Common Divisor
	The Euclidean Algorithm
	The Diophantine Equation ax+by = c

Chapter 3

Primes And Their Distribution

	The Fundamental Theorem of Arithmetic
	The Sieve of Eratosthenes
	The Goldbach Conjecture

Chapter 4

The Theory Of Congruences

4-2	Basic Properties of Congruence
4-3	Binary and Decimal Representations of Integers
4-4	Linear Congruence and the Chinese Remainder Theorem

Chapter 5

Fermat's Theorem

	Fermat's Little Theorem and Pseudoprimes
	Wilson's Theorem
	The Fermat-Kraitchik Factorization Method

Chapter 6

Number-Theoretic Functions

6-1	The Sum and Number of Divisors	Download PDF 🔻
6-2	The Mobius Inversion Formula	Download PDF 🔻
6-3	The Greatest Integer Function	Download PDF 🔻
6-4	An Application to the Calendar	Download PDF 🔻

Chapter 7

Euler's Generalization Of Fermat's Theorem

7-2	Euler's Phi-Function	Download PDF 🔻
7-3	Euler's Theorem	Download PDF 🔻
7-4	Some Properties of the Phi-Function	Download PDF 🔻

Chapter 8

Primitive Roots And Indices

8-1	The Order of an Integer Modulo n	Download PDF 🔻
8-2	Primitive Roots for Primes	Download PDF 🔻
8-3	Composite Numbers Having Primitive Roots	Download PDF 🔻
8-4	The Theory of Indices	Download PDF 🔻

Chapter 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

Chapter 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

Chapter 11

Numbers Of Special Form

11-2	Perfect Numbers
11-3	Mersenne Primes and Amicable Numbers
11-4	Fermat Numbers

Chapter 12

Certain Nonlinear Diophantine Equations

12-1	The Equation x2 + y2 = z2
12-2	Fermat's Last Theorem

Chapter 13

Representation Of Integers As Sums Of Squares

13-2	Sums of Two Squares
13-3	Sums of More Than Two Squares

Chapter 14

Fibonacci Numbers

14-2	The Fibonacci Sequence	Problems	p.291
14-3	Certain Identities Involving Fibonacci Numbers	Problems	p.299

Chapter 15

Continued Fractions

15-2	Finite Continued Fractions	Problems	p.318
15-3	Infinite Continued Fractions	Problems	p.332
15-4	Farey Fractions	Problems	p.337
15-5	Pell's Equation	Problems	p.350

Chapter 16

Some Modern Developments

16-2	Primality Testing and Factorization	Problems	p.370
16-3	An Application to Factoring: Remote Coin Flipping	Problems	p.374
		Miscellaneous Problems	p.384