The Higher Arithmetic - an Introduction to the Theory of Numbers
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Now into its eighth edition and with additional material on primality testing, written by J. H. Davenport, The Higher Arithmetic introduces concepts and theorems in a way that does not require the reader to have an in-depth knowledge of the theory of numbers but also touches upon matters of deep mathematical significance. A companion website (www.cambridge.org/davenport) provides more details of the latest advances and sample code for important algorithms. Reviews of earlier editions: ‘. . . the well-known and charming introduction to number theory . . . can be recommended both for independent study and as a reference text for a general mathematical audience.’ European Maths Society Journal ‘Although this book is not written as a textbook but rather as a work for the general reader, it could certainly be used as a textbook for an undergraduate course in number theory and, in the reviewer’s opinion, is far superior for this purpose to any other book in English.’ Bulletin of the American Mathematical Society
THE HIGHER ARITHMETIC
AN INTRODUCTION TO THE THEORY OF NUMBERS
Eighth edition
H. Davenport
M.A., SC.D., F.R.S.
late Rouse Ball Professor of Mathematics in the University of Cambridge and Fellow of Trinity College Editing and additional material by
James H. Davenport
CAMBRIDGE UNIVERSITY PRESS
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521722360 © The estate of H. Davenport 2008 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format 2008
Now into its eighth edition and with additional material on primality testing, written by J. H. Davenport, The Higher Arithmetic introduces concepts and theorems in a way that does not require the reader to have an in-depth knowledge of the theory of numbers but also touches upon matters of deep mathematical significance. A companion website (www.cambridge.org/davenport) provides more details of the latest advances and sample code for important algorithms. Reviews of earlier editions: ‘. . . the well-known and charming introduction to number theory . . . can be recommended both for independent study and as a reference text for a general mathematical audience.’ European Maths Society Journal ‘Although this book is not written as a textbook but rather as a work for the general reader, it could certainly be used as a textbook for an undergraduate course in number theory and, in the reviewer’s opinion, is far superior for this purpose to any other book in English.’ Bulletin of the American Mathematical Society
THE HIGHER ARITHMETIC
AN INTRODUCTION TO THE THEORY OF NUMBERS
Eighth edition
H. Davenport
M.A., SC.D., F.R.S.
late Rouse Ball Professor of Mathematics in the University of Cambridge and Fellow of Trinity College Editing and additional material by
James H. Davenport
CAMBRIDGE UNIVERSITY PRESS
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521722360 © The estate of H. Davenport 2008 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format 2008
References: Bibliography SIERPINSKI, W., Elementary Theory of Numbers (P.W.N., Warsaw, 1964); A Selection of Problems in the Theory of Numbers (Pergamon Press, 1964) USPENSKY, J FRENCH CAHEN, E., Th´ orie des nombres (2 vols., Hermann, Paris, 1924) e