证明哥德巴赫猜想的原文(英文)并附译后汉语

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1、此文发表在：AdvancesinTheoreticalandAppliedMathematics(ATAM),ISSN0793-4554,Vol.7,№4,2012,pp.417-424ProvingGoldbach’sConjecturebyTwoNumberAxes’PositiveHalfLineswhichReversefromEachOther’sDirectionsZhangTianshuNanhaiwestoilcorporation,ChinaoffshorePetroleum,Zhanjiangcity,Guangdongprovinc

2、e,P.R.ChinaEmail:tianshu_zhang507@aliyun.com;AbstractWeknowthateverypositiveevennumber2n(n≥3)canexpressinasumwhich3plusanoddnumber2k+1(k≥1)makes.Andthen,foranyoddpoint2k+1(k≥1)atthenumberaxis,if2k+1isanoddprimepoint,ofcourseevennumber3+(2k+1)isequaltothesumwhichoddprimenumber2k+1

3、plusoddprimenumber3makes;If2k+1isanoddcompositepoint,thenlet3

4、onvertedtoprovetherebecertainlysuchanoddprimepointBatthenumberaxis’salinesegmentwhichtakeoddpoint3andoddpoint2k+1asends,soastoprovetheconjecturebysuchamethodindirectly.KeywordsNumbertheory,Goldbach’sConjecture,Evennumber,Oddprimenumber,Mathematicalinduction,Twonumberaxes’positive

5、halflineswhichreversefromeachother’sdirection,OD,PL,CL,andRPL.BasicConcepts23Goldbach’sconjecturestatesthateveryevennumber2Nisasumoftwoprimenumbers,andeveryoddnumber2N+3isasumofthreeprimenumbers,whereN≥2.WeshallprovetheGoldbach’sconjecturethereinafterbyoddpointsattwonumberaxes’po

6、sitivehalflineswhichreversefromeachother’sdirectionsandwhichbeginwithoddpoint3.Firstwemustunderstandlistedbelowbasicconceptsbeforetheproofoftheconjecture,inordertoapplythemintheproof.Axiom．Eachandeveryevennumber2n(n≥3)canexpressinasumwhich3pluseachoddnumber2k+1(k≥1)makes.Definiti

7、on1．Alinesegmentwhichtakestwooddpointsastwoendsatthenumberaxis’spositivehalflinewhichbeginswithoddpoint3iscalledanodddistance.“OD”isabbreviatedfrom“odddistance”.TheODbetweenoddpointNandoddpointN+2tiswrittenasODN(N+2t),whereN≥3,andt≥1.AintegerwhichthelengthofODbetweentwoconsecutiv

8、eoddpointsexpressesis2.AlengthofODbetwee