a concise introduction to the theory of numbers- baker a.

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1、AconciseintroductiontothetheoryofnumbersALANBAKERProfessorofPureMathematicsintheUniversityofCambtidgeCAMBRIDGEUNIVERSITYPRESSCambrfdgeLondonNewYorkNewRochelleMelbourneSydneyContentsPublishedbythePressSyndicateoftheUniversityofCambridgePrefaceThePittB

2、uilding,TrumpingtonStreet,CambridgeCB21RP32East57thStreet,NewYork,NY10022,USAIntroduction:Gaussandnumbertheoty296BeaconsfieldParade,MiddlePark,Melbourne3206,AustraliaDivisibility@CambridgeUniversityPress1984FoundationsDivisionalgorithmFirstpublished1

3、984GreatestcommondivisorEuclid'salgorithmPrintedinGreatBritainbyFundamentaltheoremJ.W.ArrowsmithLtd.,BristolBS32NTPropertiesoftheprimesLibraryofCongresscataloguecardnumber:84-1911FurtherreadingExercisesBritishLitnutycataloguinginpublicationdataArithm

4、eticalfunctionsBaker,AlanAconciseintroductiontothetheoryofThefunction[x]numbersMultiplicativefunctions1.Numbers,TheoryofEuler's(totient)function4(n)I.TitleTheMiibiusfunctionp(n)5W.7QA241Thefunctions~(n)andu(n)ISBN0521243831hardcoversAverageordersISBN

5、0521286549paperbackPerfectnumbersTheRCemannzeta-functionFurtherreadingExercisesCongruencesDefinitionsChineseremaindertheoremThetheoremsofFermatandEulerAS.Wilson'stheoremContentsviiContents6TheGaussianfieldLagrange'stheorem7FurtherreadingPrimitiveroot

6、s8ExercisesIndicesFurtherreadingDiophantineequationsExercisesThePel1equationTheThueequationQuadraticresiduesTheMordellequationLegendre'ssymbolTheFermatequationEuler'scriterionTheCatalanequationGauss'lemmaFurtherreadingLawofquadraticreciprocityExercis

7、esJacobi'ssymbolFurtherreadingExercisesQuadraticformsEquivalenceReductionRepresentationsbybinaryformsSumsoftwosquaresSumsoffoursquaresFurtherreadingExercisesDiophantineapproximationDirichlet'stheoremContinuedfractionsRationalapproximationsQuadraticir

8、rationalsLiouville'stheoremTranscendentalnumbersMinkowski'stheoremFurtherreadingExercisesQuadraticfieldsAlgebraicnumberfieldsThequadraticfieldUnitsPrimesandfactorizationEuclideanfieldsPrefaceIthasbeencustomaryinCambridgeformanyyearstoincludeaspartoft