Elementary number theory and its applications

摘要: P. What is Number Theory? 1. The Integers. Numbers and Sequences. Sums Products. Mathematical Induction. Fibonacci Numbers. 2. Integer Representations Operations. of Computer Operations with Complexity 3. Primes Greatest Common Divisors. Prime Distribution Primes. Euclidean Algorithm. Fundemental Theorem Arithmetic. Factorization Methods Fermat Linear Diophantine Equations. 4. Congruences. Introduction to Congrences. Chinese Remainder Theorem. Solving Polynomial Systems Factoring Using the Pollard Rho Method. 5. Applications Divisibility Tests. perpetual Calendar. Round Robin Tournaments. Hashing Functions. Check Digits. 6. Some Special Wilson's Fermat's Little Pseudoprimes. Euler's 7. Multiplicative Euler Phi-Function. Sum Perfect Mersenne Mobius Inversion. 8. Cryptology. Character Ciphers. Block Stream Exponentiation Knapsack Cryptographic Protocols Applications. 9. Primitive Roots. Order an Roots for Existence Index Primality Tests Orders Integers Universal Exponents. 10. Integer. Pseudorandom EIGamal Cryptosystem. An Application Splicing Telephone Cables. 11. Quadratic Residues. Residues nonresidues. Law Reciprocity. Jacobi Symbol. Zero-Knowledge Proofs. 12. Decimal Fractions Continued. Fractions. Finite Continued Infinite Periodic 13. Nonlinear Pythagorean Triples. Last Squares. Pell's Equation. 14. Gaussian Unique