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1、NUMBERTHEORYAnIntroductiontoMathematics:PartBNUMBERTHEORYAnIntroductiontoMathematics:PartBBYWILLIAMA.COPPELQ-SpringerLibraryofCongressControlNumber:2005934653PARTAISBN-10:0-387-29851-7e-ISBN:0-387-29852-5ISBN-13:978-0387-29851-1PARTBISBN-10:0-387-29853-3e-IS
2、BN:0-387-29854-1ISBN-13:978-0387-29853-52-VOLUMESETISBN-10:0-387-30019-8e-ISBN:0-387-30529-7ISBN-13:978-0387-30019-1Printedonacid-freepaperAMSSubiectClassifications:11-xx.05820.33E05O2006SpringerScience+BusinessMedia,IncAUrightsreserved.Thisworkmaynotbetrans
3、latedorcopiedinwholeorinpartwithoutthewrittenpermissionofthepublisher(SpringerScience+BusinessMedia,Inc.,233SpringStreet,NewYork,NY10013,USA),exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.Useinconnectionwithanyformofinformationstorageandre
4、trieval,clcctronicadaptation,computersoftware,orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden.Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,eveniftheyarenotidentifiedassuch,isnottobetakenasanexpressiono
5、fopinionastowhetherornottheyaresubjecttoproprietruyrights.PrintedintheUnitedStatesofAmericaContentsPartAPrefaceITheexpandinguniverseofnumbersSets,relationsandmappingsNaturalnumbersIntegersandrationalnumbersRealnumbersMetricspacesComplexnumbersQuaternionsando
6、ctonionsGroupsRingsandfieldsVectorspacesandassociativealgebrasInnerproductspacesFurtherremarks12SelectedreferencesI1Divisibility1Greatestcommondivisors2TheBezoutidentity3Polynomials4Euclideandomains5Congruences6Sumsofsquares7Furtherremarks8Selectedreferences
7、ContentsI11Moreondivisibility1Thelawofquadraticreciprocity2Quadraticfields3Multiplicativefunctions4LinearDiophantineequations5Furtherremarks6SelectedreferencesIVContinuedfractionsandtheiruses1Thecontinuedfractionalgorithm2Diophantineapproximation3Periodiccon
8、tinuedfractions4QuadraticDiophantineequations5Themodulargroup6Non-Euclideangeometry7Complements8Furtherremarks9SelectedreferencesVHadamard'sdeterminantproblem1Whatisadeterminant?2Hadamardmatrice
