vi CONTENTS
Chapter 7. Distribution in Finite Fields and Residue Rings 117
7.1. Distribution in Finite Fields 117
7.2. Distribution in Residue Rings 119
Chapter 8. Distribution Modulo 1 and Matrix Exponential Functions 127
8.1. Main Definitions and Metric Results 127
8.2. Explicit Constructions 130
8.3. Other Problems 134
Chapter 9. Applications to Other Sequences 139
9.1. Algebraic and Exponential Polynomials 139
9.2. Linear Recurrence Sequences and Continued Fractions 145
9.3. Combinatorial Sequences 150
9.4. Solutions of Diophantine Equations 157
Chapter 10. Elliptic Divisibility Sequences 163
10.1. Elliptic Divisibility Sequences 163
10.2. Periodicity 164
10.3. Elliptic Curves 165
10.4. Growth Rates 167
10.5. Primes in Elliptic Divisibility Sequences 169
10.6. Open Problems 174
Chapter 11. Sequences Arising in Graph Theory and Dynamics 177
11.1. Perfect Matchings and Recurrence Sequences 177
11.2. Sequences arising in Dynamical Systems 179
Chapter 12. Finite Fields and Algebraic Number Fields 191
12.1. Bases and other Special Elements of Fields 191
12.2. Euclidean Algebraic Number Fields 196
12.3. Cyclotomic Fields and Gaussian Periods 202
12.4. Questions of Kodama and Robinson 205
Chapter 13. Pseudo-Random Number Generators 211
13.1. Uniformly Distributed Pseudo-Random Numbers 211
13.2. Pseudo-Random Number Generators in Cryptography 220
Chapter 14. Computer Science and Coding Theory 231
14.1. Finite Automata and Power Series 231
14.2. Algorithms and Cryptography 241
14.3. Coding Theory 247
Sequences from the on-line Encyclopedia 255
Bibliography 257
Index
309
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