## Algorithmic Number Theory |

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### Contents

Introduction | 1 |

Intractable Problems will cover the following topics | 3 |

Fundamentals of Number Theory | 19 |

Copyright | |

9 other sections not shown

### Common terms and phrases

algebraic number algorithmic number arithmetic Assume ERH asymptotic Bach Berlekamp binary bit complexity bit operations bound Carmichael numbers Chapter Chinese remainder theorem coefficients composite numbers compute congruences conjecture constant continued fraction corollary cyclic D. H. Lehmer defined denote the number deterministic polynomial discussed element equation estimate Euclidean algorithm Euler example Exercise Fermat finite fields formula gcd(a given greatest common divisor H. W. Lenstra Hence heuristic induction input irreducible polynomial lemma linear machine Math Mersenne method modulo monic polynomial multiplication nonzero number field number of primes number theory polynomial of degree polynomial-time Pomerance positive integers primality testing prime factorization prime number theorem primitive root probabilistic problem proof pseudoprime quadratic nonresidue randomized algorithm reader relatively prime result Riemann hypothesis ring root of unity running Shallit Show sieve solution square roots squarefree steps subgroup Suppose tt(x zeroes zeta function