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1、www.GetPedia.com*Morethan150,000articlesinthesearchdatabase*LearnhowalmosteverythingworksADVANCEDNUMBERTHEORYHarveyCohnDistinguishedProfessorofMathematicsCityUniversityofNewYorkDoverPublications,Inc.NewYorkdedicatedtoTONYandSUSANCopyright01962byHarveyCohn.Allrightsr
2、eservedunderPanAmericanandInter-nationalCopyrightConventions.PublishedinCanadabyGeneralPublishingCom-pany,Ltd.,30LesmillRoad,DonMills,Toronto,On-tario.PublishedintheUnitedKingdombyConstableandCompany,Ltd.,10OrangeStreet,LondonWC2H7EG.ThisDoveredition,firstpublishedi
3、n1980,isanun-abridgedandcorrectedrepublicationoftheworkfirstpublishedin1962byJohnWiley&Sons,Inc.,underthetitleASecondCourseinNumberTheory.InternationalStandardBookNumber:0-486-64023-XLibraryofCongresCatalogCordNumber:BO-65862ManufacturedintheUnitedStatesofAmericaDov
4、erPublications,Inc.100VarickStreetNewYork.N.Y.10014PREFACETheprerequisitesforthisbookarethe“standard”first-semestercourseinnumbertheory(withincidentalelementaryalgebra)andelementarycalculus.Thereisnolackofsuitabletextsfortheseprerequisites(forexample,AnIntroductiont
5、otheTheoryofNumbers,by1.NivenandH.S.Zuckerman,JohnWileyandSons,1960,caribecitedasabookthatintro-ducesthenecessaryalgebraaspartofnumbertheory).Usually,verylittleelsecaribemanagedinthatfirstsemesterbeyondthetransitionfromimprovisedcombinatorialamusementsofantiquitytot
6、hecoherentlyorganizedbackgroundforquadraticreciprocity,whichwasachievedintheeighteenthCentury.Thepresenttextconstitutesslightlymorethanenoughforasecond-semestercourse,carryingthestudentontothetwentiethCenturybymotivatingsomeheroicnineteenth-Centurydevelopmentsinalge
7、braandanalysis.TherelationofthistextbooktothegreattreatisesWillnecessarilybelikethatofahisforicalnoveltochronicles.WehopethatoncethestudentknowswhattoseekheWillfind“chronicles”tobeasexcitingasa“historicalnovel.”Theproblemsinthetextplayasignificantroleandareintendedt
8、ostimulatethespiritofexperimentationivhichhastraditionallyrulednumbertheoryandwhichhasindeedbecomeresurgentwiththerealizationofthemodernco
