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1、ADVANCEDNUMBERTHEORYHarveyCohnDistinguishedProfessorofMathematicsCityUniversityofNewYorkDoverPublications,Inc.NewYorkdedicatedtoTONYandSUSANCopyright01962byHarveyCohn.AllrightsreservedunderPanAmericanandInter-nationalCopyrightConventions.PublishedinCa
2、nadabyGeneralPublishingCom-pany,Ltd.,30LesmillRoad,DonMills,Toronto,On-tario.PublishedintheUnitedKingdombyConstableandCompany,Ltd.,10OrangeStreet,LondonWC2H7EG.ThisDoveredition,firstpublishedin1980,isanun-abridgedandcorrectedrepublicationoftheworkfirs
3、tpublishedin1962byJohnWiley&Sons,Inc.,underthetitleASecondCourseinNumberTheory.InternationalStandardBookNumber:0-486-64023-XLibraryofCongresCatalogCordNumber:BO-65862ManufacturedintheUnitedStatesofAmericaDoverPublications,Inc.100VarickStreetNewYork.N.
4、Y.10014PREFACETheprerequisitesforthisbookarethe“standard”first-semestercourseinnumbertheory(withincidentalelementaryalgebra)andelementarycalculus.Thereisnolackofsuitabletextsfortheseprerequisites(forexample,AnIntroductiontotheTheoryofNumbers,by1.Niven
5、andH.S.Zuckerman,JohnWileyandSons,1960,caribecitedasabookthatintro-ducesthenecessaryalgebraaspartofnumbertheory).Usually,verylittleelsecaribemanagedinthatfirstsemesterbeyondthetransitionfromimprovisedcombinatorialamusementsofantiquitytothecoherentlyor
6、ganizedbackgroundforquadraticreciprocity,whichwasachievedintheeighteenthCentury.Thepresenttextconstitutesslightlymorethanenoughforasecond-semestercourse,carryingthestudentontothetwentiethCenturybymotivatingsomeheroicnineteenth-Centurydevelopmentsinalg
7、ebraandanalysis.TherelationofthistextbooktothegreattreatisesWillnecessarilybelikethatofahisforicalnoveltochronicles.WehopethatoncethestudentknowswhattoseekheWillfind“chronicles”tobeasexcitingasa“historicalnovel.”Theproblemsinthetextplayasignificantrol
8、eandareintendedtostimulatethespiritofexperimentationivhichhastraditionallyrulednumbertheoryandwhichhasindeedbecomeresurgentwiththerealizationofthemoderncomputer.Astudentcompletingthiscourseshouldacquireanappreciationforthehistoricaloriginsofli
