## Elementary Number Theory and Its ApplicationsThe 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. |

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### Contents

What is Number Theory? | 1 |

Integer Representations and Operations | 39 |

Primes and Greatest Common Divisors | 65 |

Copyright | |

15 other sections not shown

### Common terms and phrases

arithmetic base b expansion bit operations Carmichael number cipher ciphertext computation program Computational and Programming Computations and Explorations conjecture Corollary cryptosystem decimal expansion decrypting diophantine equation divides division algorithm encrypted Euclidean algorithm Euler pseudoprime exponent Fermat numbers Fermat's little theorem Fibonacci numbers following computations formula function greatest common divisor Hence incongruent solutions inverse law of quadratic least positive residue Lemma linear congruences Maple or Mathematica mathematical induction Mersenne primes method multiplicative notation number theory obtain odd prime pairs plaintext polynomial 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 numbers Pythagorean triple quadratic irrational quadratic nonresidue quadratic reciprocity quadratic residue rational numbers real number relatively prime residues modulo Section sequence Show simple continued fraction strong pseudoprime Suppose