## 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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#### LibraryThing Review

User Review - zaz360 - LibraryThingThis was a good book for my Introduction to Number Theory class where we went through the first five chapters. I thought it was easy to understand and follow in working through the problems. I never got too lost or needed too much teacher explanation of the text. Pretty good overall. Read full review

### Contents

Divisibility | 1 |

Congruences | 20 |

Quadratic Reciprocity | 63 |

Copyright | |

10 other sections not shown

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### Common terms and phrases

algebraic integer algebraic number arithmetic function complete residue system complex numbers congruence convergent Corollary defined Definition density digit distinct prime divides divisible elements equation example Farey sequence finite number follows Gaussian integers greatest common divisor hence identity implies inequality infinite integral coefficients inverse irrational number isomorphic least positive Lemma mathematical induction monic polynomial natural density number of positive number of solutions number theory obtain odd prime off(x pairs perfect square polynomial positive divisors positive integers positive solution power series prime factors primitive root PROBLEMS proof of Theorem Prove quadratic field quadratic residue rational integers rational number rational prime real numbers reduced form reduced residue system relatively prime residue system modulo result satisfying Schnirelmann density Section set of integers simple continued fraction solutions of x2 solvable Solve square-free summands suppose unique factorization property values write zero