## An Introduction to the Theory of NumbersThis is the fifth edition of a work (first published in 1938) which has become the standard introduction to the subject. The book has grown out of lectures delivered by the authors at Oxford, Cambridge, Aberdeen, and other universities. It is neither a systematic treatise on the theory ofnumbers nor a 'popular' book for non-mathematical readers. It contains short accounts of the elements of many different sides of the theory, not usually combined in a single volume; and, although it is written for mathematicians, the range of mathematical knowledge presupposed is not greater thanthat of an intelligent first-year student. In this edition the main changes are in the notes at the end of each chapter; Sir Edward Wright seeks to provide up-to-date references for the reader who wishes to pursue a particular topic further and to present, both in the notes and in the text, areasonably accurate account of the present state of knowledge. |

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### Contents

THE SERIES OF PRIMES | 1 |

THE SERIES OF PRIMES | 12 |

FAREY SERIES AND A THEOREM OF MINKOWSKI | 23 |

IRRATIONAL NUMBERS | 38 |

CONGRUENCES AND RESIDUES | 48 |

FERMATS THEOREM AND ITS CONSEQUENCES | 63 |

GENERAL PROPERTIES OF CONGRUENCES | 82 |

THE REPRESENTATION OF NUMBERS BY DECIMALS | 107 |

QUADRATIC FIELDS | 218 |

THE ARITHMETICAL FUNCTIONS fn in dn 7n rn | 233 |

GENERATING FUNCTIONS OF ARITHMETICAL FUNCTIONS | 244 |

THE ORDER OF MAGNITUDE OF ARITHMETICAL FUNCTIONS | 260 |

PARTITIONS | 273 |

THE REPRESENTATION OF A NUMBER BY TWO | 297 |

REPRESENTATION BY CUBES AND HIGHER POWERS | 317 |

THE SERIES OF PRIMES | 340 |

CONTINUED FRACTIONS | 129 |

APPROXIMATION OF IRRATIONALS BY RATIONALS | 154 |

THE FUNDAMENTAL THEOREM OF ARITHMETIC IN kl | 178 |

SOME DIOPHANTINE EQUATIONS | 190 |

QUADRATIC FIELDS | 204 |

KRONECKERS THEOREM | 375 |

APPENDIX | 414 |

420 | |

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### Common terms and phrases

absolutely convergent algebraic number algorithm argument arithmetic coefficients congruence conjecture contradiction convergent convex coordinates coprime corresponding cubes D. H. Lehmer decimal deduce defined definition digits divides divisible equation equivalent Euclid's Euclid's algorithm Euclidean Euler example Farey Farey series Fermat's theorem follows formula function fundamental theorem Gauss Gaussian integers give Hence Theorem infinite infinity integral quaternions interval irrational Journal London Math Kronecker's theorem Landau lattice point loglog Minkowski Minkowski's theorem modm modp modulus multiple non-residue notation NOTES ON CHAPTER number of primes odd prime parallelogram particular positive integers positive number prime factor problem proof of Theorem properties prove Theorem quadratic residue Ramanujan Ramanujan's sum rational integers rational prime representable result roots satisfies sequence simple continued fraction solution square suppose Theorem 44 theory of numbers trivial true unity values Wilson's theorem write

### References to this book

The Arcata conference on representations of finite groups, Part 1 Paul Fong No preview available - 1987 |