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Elementary Number Theory book cover, ISBN 9781577662242

Elementary Number Theory

by Strayer, James K.

ISBN13: 9781577662242
ISBN10: 1577662245
eBook ISBN(s): 9781478605904
Edition: Revised
Format: Hardcover
Copyright: 2001-12-01
Publisher: Waveland Pr Inc

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Table of Contents

Introduction

1

(2)

Divisibility and Factorization

3

(35)

Divisibility

3

(7)

Prime Numbers

10

(8)

Greatest Common Divisors

18

(4)

The Euclidean Algorithm

22

(4)

The Fundamental Theorem of Arithmetic

26

(10)

Concluding Remarks

36

(2)

Student Projects

36

(2)

Congruences

38

(38)

Congruences

38

(10)

Linear Congruences in One Variable

48

(6)

The Chinese Remainder Theorem

54

(5)

Wilson's Theorem

59

(4)

Fermat's Little Theorem; Pseudoprime Numbers

63

(5)

Euler's Theorem

68

(5)

Concluding Remarks

73

(3)

Student Projects

73

(3)

Arithmetic Functions

76

(27)

Arithmetic Functions; Multiplicativity

76

(5)

The Euler Phi-Function

81

(5)

The Number of Positive Divisors Function

86

(3)

The Sum of Positive Divisors Function

89

(3)

Perfect Numbers

92

(4)

The Mobius Inversion Formula

96

(5)

Concluding Remarks

101

(2)

Student Projects

101

(2)

Quadratic Residues

103

(25)

Quadratic Residues

103

(5)

The Legendre Symbol

108

(9)

The Law of Quadratic Reciprocity

117

(9)

Concluding Remarks

126

(2)

Student Projects

126

(2)

Primitive Roots

128

(26)

The Order of an Integer; Primitive Roots

128

(6)

Primitive Roots for Prime Numbers

134

(6)

The Primitive Root Theorem

140

(6)

Index Arithmetic; nth Power Residues

146

(6)

Concluding Remarks

152

(2)

Student Projects

152

(2)

Diophantine Equations

154

(27)

Linear Diophantine Equations

154

(5)

Nonlinear Diophantine Equations; a Congruence Method

159

(2)

Pythagorean Triples

161

(3)

Fermat's Last Theorem

164

(4)

Representation of an Integer as a Sum of Squares

168

(11)

Concluding Remarks

179

(2)

Student Projects

180

(1)

Continued Fractions

181

(50)

Rational and Irrational Numbers

181

(9)

Finite Continued Fractions

190

(5)

Convergents

195

(7)

Infinite Continued Fractions

202

(12)

Eventually Periodic Continued Fractions

214

(9)

Periodic Continued Fractions

223

(5)

Concluding Remarks

228

(3)

Student Projects

229

(2)

A Few Applications

231

(20)

A Recreational Application

231

(2)

Cryptography; The RSA Encryption System

233

(6)

Primality Testing

239

(2)

Pell's Equation

241

(7)

Concluding Remarks

248

(3)

Student Projects

249

(2)

Appendices

251

(21)

A Mathematical Induction

251

(6)

B Equivalence Relations

257

(4)

C Abstract Algebra

261

(3)

D The Binomial Theorem

264

(2)

E Tables

266

(6)

Hints and Answers to Selected Exercises

272

(12)

Bibliography

284

(3)

Index

287

Supplemental Materials

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