Number theory in science and communication Book

1	Introduction	1
2	The Natural Numbers	16
3	Primes	25
4	The Prime Distribution	38
5	Fractions: Continued, Egyptian and Farey	62
6	Linear Congruences	95
7	Diophantine Equations	102
8	The Theorems of Fermat, Wilson and Euler	118
9	Euler Trap Doors and Public-Key Encryption	125
10	The Divisor Functions	135
11	The Prime Divisor Functions	142
12	Certified Signatures	154
13	Primitive Roots	156
14	Knapsack Encryption	173
15	Quadratic Residues	177
16	The Chinese Remainder Theorem and Simultaneous Congruences	190
17	Fast Transformation and Kronecker Products	199
18	Quadratic Congruences	203
19	Pseudoprimes, Poker and Remote Coin Tossing	205
20	The Mobius Function and the Mobius Transform	216
21	Generating Functions and Partitions	224
22	Cyclotomic Polynomials	232
23	Linear Systems and Polynomials	247
24	Polynomial Theory	250
25	Galois Fields	256
26	Spectral Properties of Galois Sequences	269
27	Random Number Generators	283
28	Waveforms and Radiation Patterns	289
29	Number Theory, Randomness and "Art"	301
30	Self-Similarity, Fractals, Deterministic Chaos and a New State of Matter	311
	Glossary of Symbols	336
	References	339
	Name Index	351
	Subject Index	355