Number Theory in Science and Communication

Number Theory in Science and Communication is an introduction for non-mathematicians. The book stresses intuitive understanding rather than abstract theory and highlights important concepts such as continued fractions, the golden ratio, quadratic residues and Chinese remainders, trapdoor functions, pseudoprimes and primitive elements. Their applications to problems in the real world is one of the main themes of the book. This third edition is augmented by recent advances in primes in progressions, twin primes, prime triplets, prime quadruplets and quintruplets, factoring with elliptic curves, quantum factoring, Golomb rulers and "baroque" integers. TOC:Introduction.- The Natural Numbers.- Primes.- The Prime Distribution.- Fractions: Continued, Egyptian and Farey.- Linear Congruences.- Diophantine Equations.- The Theorems of Fermat, Wilson and Euler.- 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.- 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".