## Elementary number theory and its applicationsElementary Number Theory and Its Applicationsis noted for its outstanding exercise sets, including basic exercises, exercises designed to help students explore key concepts, and challenging exercises. Computational exercises and computer projects are also provided. In addition to years of use and professor feedback, the fifth edition of this text has been thoroughly checked to ensure the quality and accuracy of the mathematical content and the exercises. The blending of classical theory with modern applications is a hallmark feature of the text. The Fifth Edition builds on this strength with new examples and exercises, additional applications and increased cryptology coverage. The author devotes a great deal of attention to making this new edition up-to-date, incorporating new results and discoveries in number theory made in the past few years. |

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### Contents

What Is Number Theory? | 1 |

Integer Representations and Operations | 43 |

Primes and Greatest Common Divisors | 67 |

Copyright | |

34 other sections not shown

### Common terms and phrases

arithmetic base b expansion bit operations Carmichael number check digit ciphertext computation program Computational and Programming computations and explorations conjecture decimal digits decrypting divides division algorithm encrypted Euclidean algorithm Euler exponent Fermat numbers Fermat's little theorem Fibonacci numbers following computations formula function Gaussian integers Gaussian primes greatest common divisor Hence incongruent solutions infinitely many primes inverse least positive residue Lemma letters linear congruences Maple or Mathematica mathematical induction mathematician Mersenne primes method multiplicative notation number theory obtain odd prime pairs plaintext plaintext message polynomial preamble to Exercise primality test prime divisor prime factorization prime number prime-power factorization primitive root modulo Programming Exercises Computations Programming Projects Write programs using Maple Projects Write programs proof prove pseudorandom pseudorandom numbers public key quadratic residue rational numbers real number relatively prime residues modulo Section sequence Show simple continued fraction square strong pseudoprime Suppose values Vigenere cipher