Number Theory in Science and Communication

A Few Fundamentals.- The Natural Numbers.- Primes.- The Prime Distribution.- Some Simple Applications.- Fractions: Continued, Egyptian and Farey.- Congruences and the Like.- Linear Congruences.- Diophantine Equations.- The Theorems of Fermat Wilson and Euler.- Permutations Cycles and Derangements.- Cryptography and Divisors.- Euler Trap Doors and Public-Key Encryption.- The Divisor Functions.- The Prime Divisor Functions.- Certified Signatures.- Primitive Roots.- Knapsack Encryption.- Residues and Diffraction.- Quadratic Residues.- Chinese and Other Fast Algorithms.- The Chinese Remainder Theorem and Simultaneous Congruences.- Fast Transformation and Kronecker Products.- Quadratic Congruences.- Pseudoprimes, Möbius Transform, and Partitions.- Pseudoprimes Poker and Remote Coin Tossing.- The Möbius Function and the Möbius Transform.- Generating Functions and Partitions.- From Error Correcting Codes to Covering Sets.- Cyclotomy and Polynomials.- Cyclotomic Polynomials.- Linear Systems and Polynomials.- Polynomial Theory.- Galois Fields and More Applications.- Galois Fields.- Spectral Properties of Galois Sequences.- Random Number Generators.- Waveforms and Radiation Patterns.- Number Theory Randomness and "Art".- Self-Similarity, Fractals and Art.- Self-Similarity, Fractals, Deterministic Chaos and a New State of Matter.