## An Introduction to the Theory of NumbersAn Introduction to the Theory of Numbers by G.H. Hardy and E. M. Wright is found on the reading list of virtually all elementary number theory courses and is widely regarded as the primary and classic text in elementary number theory. Developed under the guidance of D.R. Heath-Brown this Sixth Edition of An Introduction to the Theory of Numbers has been extensively revised and updated to guide today's students through the key milestones and developments in number theory. Updates include a chapter by J.H. Silverman on one of the most important developments in number theory — modular elliptic curves and their role in the proof of Fermat's Last Theorem — a foreword by A. Wiles, and comprehensively updated end-of-chapter notes detailing the key developments in number theory. Suggestions for further reading are also included for the more avid reader The text retains the style and clarity of previous editions making it highly suitable for undergraduates in mathematics from the first year upwards as well as an essential reference for all number theorists. |

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### Contents

I THE SERIES OF PRIMES 1 | 1 |

II THE SERIES OF PRIMES 2 | 14 |

III FAREY SERIES AND A THEOREM OF MINKOWSKI | 28 |

IV IRRATIONAL NUMBERS | 45 |

V CONGRUENCES AND RESIDUES | 57 |

VI FERMATS THEOREM AND ITS CONSEQUENCES | 78 |

VII GENERAL PROPERTIES OF CONGRUENCES | 103 |

VIII CONGRUENCES TO COMPOSITE MODULI | 120 |

XVII GENERATING FUNCTIONS OF ARITHMETICAL FUNCTIONS | 318 |

XVIII THE ORDER OF MAGNITUDE OF ARITHMETICAL FUNCTIONS | 342 |

XIX PARTITIONS | 361 |

XX THE REPRESENTATION OF A NUMBER BY TWO OR FOUR SQUARES | 393 |

XXI REPRESENTATION BY CUBES AND HIGHER POWERS | 419 |

XXII THE SERIES OF PRIMES 3 | 451 |

XXIII KRONECKERS THEOREM | 501 |

XXIV GEOMETRY OF NUMBERS | 523 |

IX THE REPRESENTATION OF NUMBERS BY DECIMALS | 138 |

X CONTINUED FRACTIONS | 165 |

XI APPROXIMATION OF IRRATIONALS BY RATIONALS | 198 |

XII THE FUNDAMENTAL THEOREM OF ARITHMETIC IN k1 ki AND k961 | 229 |

XIII SOME DIOPHANTINE EQUATIONS | 245 |

XIV QUADRATIC FIELDS 1 | 264 |

XV QUADRATIC FIELDS 2 | 283 |

XVI THE ARITHMETICAL FUNCTIONS 216n 956n dn 963n rn | 302 |

XXV ELLIPTIC CURVES | 549 |

Appendix | 593 |

A List of Books | 597 |

Index of Special Symbols and Words | 601 |

605 | |

611 | |

### Other editions - View all

An Introduction to the Theory of Numbers G. H. Hardy,E. M. Wright,Joseph Silverman,Andrew Wiles No preview available - 2008 |

An Introduction to the Theory of Numbers G. H. Hardy,E. M. Wright,Roger Heath-Brown,Joseph Silverman No preview available - 2008 |

An Introduction to the Theory of Numbers Godfrey H. Hardy,Edward M. Wright No preview available - 2008 |

### Common terms and phrases

algebraic algorithm approximation argument arithmetic associate belongs bound chapter coefficients common complete condition congruence conjecture consider contains continued fraction convergent coordinates corresponding decimal defined definition depends divide divisible divisor elliptic curve equal equation equivalent example expressed factor Fermat’s field finite follows formulae function fundamental give given greater Hence identity important included independent integers interesting interval irrational known lattice least less London Math Math means method multiple natural obtain ofthe particular partitions points polynomial positive possible powers prime problem proof of Theorem properties prove prove Theorem quadratic rational references representable require residues result roots satisfy shows side similar simple solutions square suppose theory true unique unity values write