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9781577664451

Elementary Number Theory

by
  • ISBN13:

    9781577664451

  • ISBN10:

    1577664450

  • Edition: 2nd
  • Format: Hardcover
  • Copyright: 2006-02-15
  • Publisher: Waveland Pr Inc

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Table of Contents

Credits iii
Preface vi
What Is Number Theory?
1(12)
Divisibility
13(34)
The GCD and LCM
13(5)
The Division Algorithm
18(5)
The Euclidean Algorithm
23(4)
Linear Combinations
27(6)
Congruences
33(5)
Mathematical Induction
38(9)
Prime Numbers
47(30)
Prime Factorization
47(5)
The Fundamental Theorem of Arithmetic
52(3)
The Importance of Unique Factorization
55(5)
Prime Power Factorizations
60(5)
The Set of Primes is Infinite
65(6)
A Formula for τ(n)
71(6)
Numerical Functions
77(40)
The Sum of the Divisors
77(6)
Multiplicative Functions
83(7)
Perfect Numbers
90(4)
Mersenne and Fermat Numbers
94(7)
The Euler Phi Function
101(7)
The Mobius Inversion Formula
108(9)
The Algebra of Congruence Classes
117(42)
Solving Linear Congruences
117(8)
The Chinese Remainder Theorem
125(8)
The Theorems of Fermat and Euler
133(7)
Primality Testing
140(8)
Public-Key Cryptography
148(11)
Congruences of Higher Degree
159(36)
Polynomial Congruences
159(6)
Congruences with Prime Power Moduli
165(7)
Quadratic Residues
172(7)
Quadratic Reciprocity
179(7)
Flipping a Coin over the Telephone
186(9)
The Number Theory of the Reals
195(40)
Rational and Irrational Numbers
195(8)
Finite Continued Fractions
203(8)
Infinite Continued Fractions
211(9)
Decimal Representation
220(6)
Lagrange's Theorem and Primitive Roots
226(9)
Diophantine Equations
235(28)
Pythagorean Triples
235(7)
Sums of Two Squares
242(5)
Sums of Four Squares
247(4)
Sums of Fourth Powers
251(5)
Pell's Equation
256(7)
Bibliography 263(4)
Answers to Odd-Numbered Problems 267(8)
Index 275

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