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1、NUMBERTHEORYAnIntroductiontoMathematics:PartANUMBERTHEORYAnIntroductiontoMathematics:PartABYWILLIAMA.COPPEL-SpringerLibraryofCongressControlNumber:2005934653PARTAISBN-10:0-387-29851-7e-ISBN:0-387-29852-5ISBN-13:978-0387-29851-1PARTBISBN-10:0-387-29853-3e-ISBN:0-387-29854-1ISBN-13:978-0387-29853-5PV
2、OLUMESETISBN-10:0-387-30019-8e-ISBN:0-387-30529-7ISBN-]3:978-0387-30019-1Printedonacid-freepaper.AMSSubiectClassifications:11-xx.05820.33E05O2006SpringerScience+BusinessMedia,IncAllrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewrittenpermissionofthepublisher(SpringerScie
3、nce+BusinessMedia,Inc.,233SpringStrcct,NcwYork,NY10013,USA),exceptforbriefexccrptsinconnectionwithreviewsorscholarlyanalysis.Useinconnectionwithanyformofinformationstorageandretrieval,clcctronicadaptation,computersoftware,orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden.The
4、useinthispublicationoftradenarncs,trademarks,servicemarks,andsimilarterms,eveniftheyarenotidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubjecttoproprietaryrights.PrintedintheUnitedStatesofAmericaForJonathan,Nicholas,PhilipandStephenContentsPartAPrefaceITheexpandingun
5、iverseofnumbersSets,relationsandmappingsNaturalnumbersIntegersandrationalnumbersRealnumbersMetricspacesComplexnumbersQuaternionsandoctonionsGroupsRingsandfieldsVectorspacesandassociativealgebrasInnerproductspacesFurtherremarksSelectedreferencesI1Divisibility1Greatestcommondivisors2TheBezoutidentity
6、3Polynomials4Euclideandomains5Congruences6Sumsofsquares7Furtherremarks8Selectedreferences...VlllContentsI11Moreondivisibility1Thelawofquadraticreciprocity2Quadraticfields3Multiplicativefunctions4LinearDiophantineequations5Furtherremarks6SelectedreferencesIVContinuedfractionsandtheiruses1Thecontinue
7、dfractionalgorithm2Diophantineapproximation3Periodiccontinuedfractions4QuadraticDiophantineequations5Themodulargroup6Non-Euclideangeometry7Complements8Furtherremarks9SelectedreferencesVHadamard'sdeterminant
