## Elementary number theory and its applications |

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### Contents

The Integers | 4 |

Greatest Common Divisors and Prime Factorization | 74 |

Congruences | 119 |

Copyright | |

10 other sections not shown

### Common terms and phrases

arithmetic base b expansion bit operations Carmichael number check digit Chinese remainder theorem cipher system ciphertext composite computation program Computations and Explorations Computer Projects Programming conjecture continued fraction expansion Corollary decimal digits deciphering divides division algorithm Euclidean algorithm Euler pseudoprime Fermat numbers Fermat's little theorem Fibonacci numbers following computations following integers following theorem greatest common divisor Hence incongruent solutions infinitely integer relatively prime inverse least positive residue Lemma linear congruences mathematical induction mathematician matrix Mersenne method modp multiplicative nonnegative integer notation number theory obtain odd prime pairs perfect square prime divisor prime factorization prime-power factorization primitive root modulo Programming Projects Write Projects Programming Projects Projects Write programs Proof prove pseudo-random numbers Pythagorean triple quadratic irrational quadratic nonresidue quadratic residue quotient rational number real number relatively prime residues modulo RSA cipher Section sequence Show simple continued fraction strong pseudoprime Suppose