## Elementary number theory and its applications |

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### Contents

Introduction | 1 |

Greatest Common Divisors and Prime Factorization | 70 |

Congruences | 110 |

Copyright | |

11 other sections not shown

### Common terms and phrases

arithmetic base b expansion binary bit operations Carmichael number Chinese remainder theorem cipher system ciphertext ciphertext block Computer Projects Write conclude congruence x2 Consequently continued fraction expansion convergent Corollary decimal expansion deciphering divides division algorithm Euclidean algorithm Euler pseudoprime exponent Fermat numbers Fermat■s little theorem following theorem formula function greatest common divisor Hence incongruent solutions infinitely integer relatively prime inverse irrational number Jacobi symbol knapsack problem least positive residue Legendre symbols Lemma linear congruences mathematical induction mathematician Miller■s test modp modular exponentiation multiplicative nonnegative integers notation number theory obtain odd prime perfect number perfect square plaintext block positive integers less primality test prime divisor prime factorization prime-power factorization primitive root modulo Projects Write programs Proof prove Pythagorean triple quadratic irrational quadratic residue quotient rational number real number relatively prime residues modulo RSA cipher Section sequence Show simple continued fraction strong pseudoprime