Fundamental Number Thoery with Applications Book

Preface     ix
Arithmetic of the Integers     1
Induction     1
Division     16
Primes     30
The Chinese Remainder Theorem     40
Thue's Theorem     44
Combinatorial Number Theory     49
Partitions and Generating Functions     55
True Primality Tests     60
Distribution of Primes     65
Modular Arithmetic     73
Basic Properties     73
Modular Perspective     84
Arithmetic Functions: Euler, Carmichael, and Mobius     90
Number and Sums of Divisors     102
The Floor and the Ceiling     108
Polynomial Congruences     113
Primality Testing     119
Cryptology     127
Primitive Roots     139
Order     139
Existence     145
Indices     153
Random Number Generation     160
Public-Key Cryptography     166
Quadratic Residues     177
The Legendre Symbol     177
The Quadratic Reciprocity Law     189
Factoring     201
Simple Continued Fractions and DiophantineApproximation     209
Infinite Simple Continued Fractions     209
Periodic Simple Continued Fractions     221
Pell's Equation and Surds     232
Continued Fractions and Factoring     240
Additivity - Sums of Powers     243
Sums of Two Squares     243
Sums of Three Squares     252
Sums of Four Squares     254
Sums of Cubes     259
Diophantine Equations     265
Norm-Form Equations     265
The Equation ax[superscript 2] + by[superscript 2] + cz[superscript 2] = 0     274
Bachet's Equation     277
Fermat's Last Theorem     281
Fundamental Facts     285
Complexity     311
Primes [characters not reproducible] 9547 and Least Primitive Roots     313
Indices     318
The ABC Conjecture     319
Primes is in P     320
Solutions to Odd-Numbered Exercises     323
Bibliography     351
List of Symbols     355
Index     356
About the Author     369