tattersall j. elementary number theory in nine chapters (cup, 1999)(417s)_mt_

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1、ThispageintentionallyleftblankElementarynumbertheoryinninechaptersJAMESJ.TATTERSALLCambridge,NewYork,Melbourne,Madrid,CapeTown,Singapore,SãoPauloCambridgeUniversityPressTheEdinburghBuilding,Cambridge,UnitedKingdomPublishedintheUnitedStatesbyCambridgeUn

2、iversityPress,NewYorkwww.cambridge.orgInformationonthistitle:www.cambridge.org/9780521585033©CambridgeUniversityPress1999Thisbookisincopyright.Subjecttostatutoryexceptionandtotheprovisionofrelevantcollectivelicensingagreements,noreproductionofanypartmaytakeplacewithoutthewrittenper

3、missionofCambridgeUniversityPress.Firstpublishedinprintformat1999ISBN-13978-0-511-06583-5eBook(NetLibrary)ISBN-100-511-06583-3eBook(NetLibrary)ISBN-13978-0-521-58503-3hardbackISBN-100-521-58503-1hardbackISBN-13978-0-521-58531-6paperbackISBN-100-521-58531-7paperbackCambridgeUniversi

4、tyPresshasnoresponsibilityforthepersistenceoraccuracyofsforexternalorthird-partyinternetwebsitesreferredtointhisbook,anddoesnotguaranteethatanycontentonsuchwebsitesis,orwillremain,accurateorappropriate.ToTerryContentsPrefacevii1Theintriguingnaturalnumbers1.1Polygonalnumbers11.2S

5、equencesofnaturalnumbers221.3Theprincipleofmathematicalinduction381.4Miscellaneousexercises412Divisibility2.1Thedivisionalgorithm492.2Thegreatestcommondivisor582.3TheEuclideanalgorithm642.4Pythagoreantriples702.5Miscellaneousexercises753Primenumbers3.1Euclidonprimes793.2Numbertheor

6、eticfunctions863.3Multiplicativefunctions953.4Factoring1003.5Thegreatestintegerfunction1043.6Primesrevisited1073.7Miscellaneousexercises1224Perfectandamicablenumbers4.1Perfectnumbers1274.2Fermatnumbers135ivContentsv4.3Amicablenumbers1374.4Perfect-typenumbers1415Modulararithmetic5.1

7、Congruence1505.2Divisibilitycriteria1585.3Euler'sphi-function1625.4Conditionallinearcongruences1705.5Miscellaneousexercises1796Congruencesofhigherdegree6.1Polynomialcongruences1826.2Quadraticcongruences1866.3Primitiveroots1986.4Miscellaneousexercises2087Cryptology7.1Monoalphabeticc

8、iphers2107.2Polyalphabetic