初等數論及其應用(英文版)

What is Number Theory?
1 The Integers
1.1 Numbers and Sequesces
1.2 Sums and Products
1.3 Mathematical Induction
1.4 The Fibonacci Numbers
1.5 Divisibility
2 Integer Representations and Operations
2.1 Representations of Integers
2.2 Computer Operations with integers
2.3 Complexity of Integer Operations
3 Pringes and Greatest Common Divisors
3.1 Prime Numbers
3.2 The Distriburion of Primes
3.3 Greatest Common Divisors
3.4 The Euclidean Algorithm
3.5 The Fundamental Theorem of Arithmetic
3.6 Factorization Methods and the Fermat Numbers
3.7 Linear Diophantine Equations
4 Congruences
4.1 Introduction to Congruences
4.2 Linear Congruences
4.3 The Chinese Remainder Theorem
4.4 Solving Polynomial Congruences
4.5 Systems of Linear Congruences
4.6 Factoring Using the Pollard Rho Method
5 Applications of Congruemces
5.1 Divisibility Tests
5.2 The Perpetual Calendar
5.3 Round-Robin Tournaments
5.4 Hashing Functions
5.5 Check Digits
6 Some Special Congruences
6.1 Wilson﹀s Theorem and Fermat﹀s Little Theorem
6.2 Pseudoprimes
6.3 Euler﹀s Theorem
7 Multiplicative functions
7.1 The Euler Phi-Function
7.2 The Sum and Number of Divisors
7.3 Perfect Numbers and Mersenne Primes
7.4 Mobius Inversion
8 Cryptology
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9 Primitive Roots
10 Applications of Primitive Roots and the Order of an Integer
11 Quadratic Residues
12 Decimal Fractions and Continued Fractions
13 Some Nonlinear Diophantine Equations
14 The Gaussian Integers
A Axioms for the Set of Integers
B Binomial Coefficients
C Using Maple and Mathematica for Number Theory
D Number Theory Web Links
E Tables