# An Introduction to the Theory of Numbers

OUP Oxford, Jul 31, 2008 - Mathematics - 621 pages
An 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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point wise explained!

### 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 Index of Names 605 General Index 611 Copyright

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Roger Heath-Brown F.R.S. was born in 1952, and is currently Professor of
Pure Mathematics at Oxford University. He works in analytic number
theory, and in particular on its applications to prime numbers and to
Diophantine equations.