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1、JózsefSándorGEOMETRICTHEOREMS,DIOPHANTINEEQUATIONS,ANDARITHMETICFUNCTIONS*************************************AB/AC=(MB/MC)(sinu/sinv)1/z+1/y=1/zZ(n)isthesmallestintegermsuchthat1+2+…+misdivisiblebyn*************************************AmericanResearchP
2、ressRehoboth2002JózsefSándorDEPARTMENTOFMATHEMATICSBABEŞ-BOLYAIUNIVERSITY3400CLUJ-NAPOCA,ROMANIAGeometricTheorems,DiophantineEquations,andArithmeticFunctionsAmericanResearchPressRehoboth2002Thisbookcanbeorderedinmicrofilmformatfrom:BooksonDemandProQuest
3、InformationandLearning(UniversityofMicrofilmInternational)300N.ZeebRoadP.O.Box1346,AnnArborMI48106-1346,USATel.:1-800-521-0600(CustomerService)http://wwwlib.umi.com/bod/Copyright2002byAmericanResearchPressRehoboth,Box141NM87322,USAE-mail:M_L_Perez@yahoo
4、.comMorebooksonlinecanbedownloadedfrom:http://www.gallup.unm.edu/~smarandache/eBook-otherformats.htmReferents:A.Bege,Babeş-BolyaiUniv.,Cluj,Romania;K.Atanassov,Bulg.Acad.ofSci.,Sofia,Bulgaria;V.E.S.Szabó,TechnicalUniv.ofBudapest,Budapest,Hungary.ISBN:1-
5、931233-51-9StandardAddressNumber297-5092PrintedintheUnitedStatesofAmerica"...Itisjustthis,whichgivesthehigherarithmeticthatmagicalcharmwhichhasmadeitthefavouritescienceofthegreatestmathematicians,nottomentionitsinexhaustiblewealth,whereinitsogreatlysurp
6、assesotherpartsofmathematics..."(K.F.Gauss,Disquisitionesarithmeticae,G•ottingen,1801)1PrefaceThisbookcontainsshortnotesorarticles,aswellasstudiesonseveraltopicsofGeometryandNumbertheory.Thematerialisdividedinto vechapters:Geometricthe-orems;Diophantine
7、equations;Arithmeticfunctions;Divisibilitypropertiesofnumbersandfunctions;andSomeirrationalityresults.Chapter1dealsessentiallywithgeometricinequalitiesfortheremarkableelementsoftrianglesortetrahedrons.Otherthemeshaveanarithmeticcharacter(as9-12)onnumber
8、theoreticproblemsinGeometry.Chapter2includesvariousdiophantineequations,someofwhicharetreatablebyelementarymeth-ods;othersarepartialsolutionsofcertainunsolvedproblems.AnimportantmethodisbasedonthefamousEuler-Bell-Kalmarlemma,wit
