## An Introduction to the Theory of NumbersThe Fifth Edition of one of the standard works on number theory, written by internationally-recognized mathematicians. Chapters are relatively self-contained for greater flexibility. New features include expanded treatment of the binomial theorem, techniques of numerical calculation and a section on public key cryptography. Contains an outstanding set of problems. |

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### Contents

Divisibility | 1 |

Congruences | 20 |

Quadratic Reciprocity | 63 |

Copyright | |

11 other sections not shown

### Common terms and phrases

addition algebraic number apply arithmetic associates assume belongs called chapter common divisor complete congruence consider continued fraction convergent Corollary corresponding counted defined Definition denote density determine digit distinct divides divisible elements equal equation equivalent establish exactly example exist expansion exponent expressed fact factors field Finally finite follows formula function given gives greatest hence holds identity implies induction inequality infinite inverse least Lemma less method modulo multiplicative non-negative obtain odd prime pairs partition polynomial positive integers possible prime PROBLEMS Proof Prove Q(Vm quadratic residue rational integers rational number real numbers reduced relatively prime replaced represented result root satisfying sequence shows simple solutions Solve square Suggestion summands suppose Theorem theory unique unit values write written zero