Elementary number theory in nine chapters (2ed.，Cambridge UniversityPress 2005).pdf

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

2、ambridgeUniversityPress,NewYorkwww.cambridge.orgInformationonthistitle:www.cambridge.org/9780521850148©CambridgeUniversityPress2005Thispublicationisincopyright.Subjecttostatutoryexceptionandtotheprovisionofrelevantcollectivelicensingagreements,noreproductionof

3、anypartmaytakeplacewithoutthewrittenpermissionofCambridgeUniversityPress.Firstpublishedinprintformat2005-----eBook(NetLibrary)----eBook(NetLibrary)-----hardback----hardback----

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5、rappropriate.ContentsPrefacepageix1Theintriguingnaturalnumbers1.1Polygonalnumbers11.2Sequencesofnaturalnumbers231.3Theprincipleofmathematicalinduction401.4Miscellaneousexercises431.5Supplementaryexercises502Divisibility2.1Thedivisionalgorithm552.2Thegreatestco

6、mmondivisor642.3TheEuclideanalgorithm702.4Pythagoreantriples762.5Miscellaneousexercises812.6Supplementaryexercises843Primenumbers3.1Euclidonprimes873.2Numbertheoreticfunctions943.3Multiplicativefunctions1033.4Factoring1083.5Thegreatestintegerfunction1123.6Prim

7、esrevisited1153.7Miscellaneousexercises1293.8Supplementaryexercises133viContentsvii4Perfectandamicablenumbers4.1Perfectnumbers1364.2Fermatnumbers1454.3Amicablenumbers1474.4Perfect-typenumbers1504.5Supplementaryexercises1595Modulararithmetic5.1Congruence1615.2D

8、ivisibilitycriteria1695.3Euler’sphi-function1735.4Conditionallinearcongruences1815.5Miscellaneousexercises1905.6Supplementaryexercises1936Congruencesofhigherdegree6.1Polynomialcong