Fundamental Number Theory with Applications (Hardcover, 2 ed)

Preface
Arithmetic of the Integers
Induction
Division
Primes
The Chinese Remainder Theorem
Thue’s Theorem
Combinatorial Number Theory
Partitions and Generating Functions
True Primality Tests
Distribution of Primes
Modular Arithmetic
Basic Properties
Modular Perspective
Arithmetic Functions: Euler, Carmichael, and Mobius
Number and Sums of Divisors
The Floor and the Ceiling
Polynomial Congruences
Primality Testing
Cryptology
Primitive Roots
Order
Existence
Indices
Random Number Generation
Public-Key Cryptography
Quadratic Residues
The Legendre Symbol
The Quadratic Reciprocity Law
Factoring
Simple Continued Fractions and Diophantine Approximation
Infinite Simple Continued Fractions
Periodic Simple Continued Fractions
Pell’s Equation and Surds
Continued Fractions and Factoring
Additivity?Sums of Powers
Sums of Two Squares
Sums of Three Squares
Sums of Four Squares
Sums of Cubes
Diophantine Equations
Norm-Form Equations
The Equation ax² + by² + cz² = 0
Bachet’s Equation
Fermat’s Last Theorem
Appendix A: Fundamental Facts
Appendix B: Complexity
Appendix C: Primes ≤ 9547 and Least Primitive Roots
Appendix D: Indices
Appendix E: The ABC Conjecture
Appendix F: Primes Is in P
Solutions to Odd-Numbered Exercises
Bibliography
List of Symbols
Index