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1、ANINTRODUCTIONTOTHETHEORYOFNUMBERSANINTRODUCTIONTOTHETHEORYOFNUMBERSBYG.H.HARDYANDE.M.WRIGHTPrincipalandVice-ChancelloroftheUniversityofAberdeenFOURTHEDITIONOX.FORDATTHECLARENDONPRESSOx@dUniversityPress,ElyHouse,LondonW.1OLASOOWNEWYORKTORONTOMELBOURNEWELLINGTONCAPETOWNIBADANNAIROBIDA
2、RESSALAAMI.USAKAADDISABABADELEIBOMBAYC.4I.CUTTAMADRASKARACHILAHOREDACCAKUALALUMPURSINOAPOREHONORONOTOKYOISBN0198533107Fi&edition1938Secondeditionxg45Thirdedition1954Fourthedition1960rg6z(withcorrections)1965(withcorrections)1968(withcowectiona)=97=>1975PrintedinGreatB&ainattheUnivers
3、ityPress,OxfordbyVivianRidlerPrintertotheUniversityPREFACETOTHEFOURTHEDITIONAPARTfromtheprovisionofanindexofnames,themainchangesinthiseditionareintheNotesattheendofeachchapter.Thesehavebeenrevisedtoincludereferencestoresultspublishedsincethethirdeditionwenttopressandtocorrectomission
4、s.ThercaresimplerproofsofTheorems234,352,and357andanewTheorem272.ThePostscripttothethirdeditionnowtakesitsproperplaceaspartofChapterXX.1amindebtedtoseveralcorrespondentswhosuggestedimprovementsandcorrections.1havetothankDr.PontingforagainreadingtheproofsandMrs.V.N.R.Milneforcompiling
5、theindexofnames.E.M.W.ABERDEENJuly1959PREFACETOTHEFIRSTEDITIONTHISbookhasdevelopedgraduallyfromlecturesdeliveredinanumberofuniversitiesduringthelasttenyears,and,likemanybookswhichhavegrownoutoflectures,ithasnoverydefiniteplan.Itisnotinanysense(asanexpertcariseebyreadingthetableofcont
6、ents)asystematictreatiseonthetheoryofnumbers.Itdoesnotevencontainafullyreasonedaccountofanyonesideofthatmany-sidedtheory,butisanintroduction,oraseriesofintroductions,toalmosta11ofthesesidesinturn.Wesaysomethingabouteachofanumberofsubjectswhicharenotusuallycombinedinasinglevolume,anda
7、boutsomewhicharenotalwaysregardedasformingpartofthetheoryofnumbersatall.ThusChs.XII-XVbelongtothe‘algebraic’theoryofnumbers,Chs.XIX-XXItothe‘additive’,andCh.XXIItothe‘analytic’theories;whileChs.III,XI,XXIII,andXXIVdealwithmattersusuallyclassifiedundertheheadingsof‘geometryofnumbers’o
8、r‘Diophantin
