Number Theory in Science and Communication: With Applications in Cryptography, Physics, Digi... Book

Introduction.- The Natural Numbers.- Primes.- The Prime Distribution.- Fractions: Continued, Egyptian and Farey.- Linear Congruences.- Diophantine Equations.- The Theorems of Fermat, Wilson and Euler.- Permutation, Cycles and Derangements.- Euler Trap Doors and Public-Key Encryption.- The Divisor Functions.- The Prime Divisor Functions.- Certified Signatures.- Primitive Roots.- Knapsack Encryption.- Quadratic Residues.- The Chinese Remainder Theorem and Simultaneous Congruences.- Fast Transformations and Kronecker Products.- Quadratic Congruences.- Psudoprimes, Poker and Remote Coin Tossing.- The Möbius Function and the Möbius Transform.- From Error Correction Codes to Covering Sets.- Generating Functions and Partitions.- Cyclotomic Polynomials.- Linear Systems and Polynomials.- Polynomial Theory.- Galois Fields.- Spectral Properties of Galois Sequences.- Random Number Generators.- Waveforms and Radiation Patterns.- Number Theory, Randomness and "Art".