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Elementary number theory : and its applications / Kenneth H. Rosen

Main Author Rosen, Kenneth H. Country Estados Unidos. Edition 4th ed Publication Reading, Mass. : Addison-Wesley, cop. 2000 Description XVIII, 638 p. : il. ; 24 cm ISBN 0-201-87073-8 CDU 511
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Item type Current location Call number Status Date due Barcode Item holds Course reserves
Monografia Biblioteca Geral da Universidade do Minho
BGUM 511 - R Available 331227

Licenciatura em Ciências da Computação Teoria de Números Computacional 2º semestre

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Enhanced descriptions from Syndetics:

The fourth edition of Kenneth Rosen's widely used and successful text, Elementary Number Theory and Its Applications, preserves the strengths of the previous editions, while enhancing the book's flexibility and depth of content coverage.The blending of classical theory with modern applications is a hallmark feature of the text. The Fourth Edition builds on this strength with new examples, additional applications and increased cryptology coverage. Up-to-date information on the latest discoveries is included.Elementary Number Theory and Its Applications provides a diverse group of exercises, including basic exercises designed to help students develop skills, challenging exercises and computer projects. In addition to years of use and professor feedback, the fourth edition of this text has been thoroughly accuracy checked to ensure the quality of the mathematical content and the exercises.

Table of contents provided by Syndetics

  • 1 The Integers
  • Numbers, Sequences, and Sums
  • Mathematical Induction
  • The Fibonacci Numbers
  • Divisibility
  • 2 Integer Representation and Operations
  • Representation of Integers
  • Computer Operations with Integers
  • Complexity of Integer Operations
  • 3 Primes and Greatest Common Divisors
  • Prime Numbers
  • Greatest Common Divisors
  • The Euclidean Algorithm
  • The Fundamental Theorem of Arithmetic
  • Factorization Methods and the Fermat Numbers
  • Linear Diophantine Equations
  • 4 Congruences
  • Introduction to Congruences
  • Linear Congruences
  • The Chinese Remainder Theorem
  • Solving Polynomial Congruences
  • Systems of Linear Congruences
  • Factoring Using the Pollard rho Method
  • 5 Applications of Congruences
  • Divisibility Tests
  • The Perpetual Calendar
  • Round-Robin Tournaments
  • Hashing Functions
  • Check Digits
  • 6 Some Special Congruences
  • Wilson's Theorem and Fermat's Little Theorem
  • Pseudoprimes
  • Euler's Theorem
  • 7 Multiplicative Functions
  • Euler's Phi-Function
  • The Sum and Number of Divisors
  • Perfect Numbers and Mersenne Primes
  • Mouml;bius Inversion
  • 8 Cryptology
  • Character Ciphers
  • Block and Stream Ciphers
  • Exponentiation Ciphers
  • Public-Key Crytography
  • Knapsack Ciphers
  • Crytographic Protocols and Applications
  • 9 Primitive Roots
  • The Order of an Integer and Primitive Roots
  • Primitive Roots for Primes
  • The Existence of Primitive Roots
  • Index Arithmetic
  • Primality Testing Using Orders of Integers and Primitive Roots
  • Universal Exponents
  • 10 Applications of Primitive Roots
  • Pseudorandom Numbers
  • The E1Gamal Cryptosystem
  • An Application to the Splicing of Telephone Cables
  • 11 Quadratic Residues and Reciprocity
  • Quadratic Residues and Nonresidues
  • The Law of Quadratic Reciprocity
  • The Jacobi Symbol
  • Euler Pseudoprimes
  • Zero-Knowledge Proofs
  • 12 Decimal Fractions and Continued Fractions
  • Decimal Fractions
  • Finite Continued Fractions
  • Infinite Continued Fractions
  • Periodic Continued Fractions
  • Factoring Using Continued Fractions
  • 13 Some Nonlinear Diophantine Equations
  • Pythagorean Triples
  • Fermat's Last Theorem
  • Sums of Squares
  • Pell's Equations
  • Appendix A Axioms for the Set of Integers
  • Appendix B Binomial Coefficients
  • Appendix C Using Maplereg; and Mathematica for Number Theory
  • Appendix D Number Theory Web Links
  • Appendix E Tables
  • Answers to odd-numbered exercises
  • Bibliography
  • Index of Biographies
  • Index

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