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1、E40E4BmVol.40,No.419977AACTAMATHEMATICASINICAJuly,1997mittnwtpk&(8_O5n8210097)S51(85F?d!8210003)LH3#GN28-'!4#G+J>.*(POBE<(LH3#G"FQ8M[1–3]R/K-'!4#G(*7DI=(60uylGoldbach#G:@CB#G%A*7?,)$B9Dirichlet*7MR(1991)s
2、11N,11Ps
3、
4、O156.4OntheRepresentationofaLargeEvenIntegerastheSumofaPrimeandanAlmostPrime:ThePrimeBelongstoaFixedArithmeticSequenceShanZun(DepartmentofMathematics,NanjingNormalUniversity,Nanjing210097,China)KanJiahai(NanjingInstituteofPostsandTelecommunications,Nanjing210
5、003,China)AbstractYu’sConjectureimpliesGoldbach’sConjecture.ForYu’sConjecturewithanyfixedpositiveintegermodulus,weshowhereresultswhichareasstrongasthosetheoremsof[1–3]aboutGoldbach’sConjecture.KeywordsTheGoldbachconjecture,Thetwinprimesconjecture,Chen’stheorem
6、,Sievemethods,Arithmeticsequence,Dirichlet’stheorem1991MRSubjectClassification11N,11PChineseLibraryClassificationO156.41zv[N,S3?227、N1973[1]::%UL4'a8Goldbach?_5H−2#{p:p0.67CNNlnN
8、.(I)fYSC1995-11-14,WSC1996-11-04,hSC1996-11-19626l401990[2,3]:2L4':#{p:pCNNlnN(lnlnN),r≥3.(II)(r−2)!4(II)#>0.77−2r−2#{p:pCNNlnN(lnlnN),r≥3.(III)(r−2)!-9、'HHMIrH?L4HH?L4^9),K(I)(II)(III)Y?skpD%@j}XpMc6ZA"k(?K[a,bKJkϕEulerlk?^"f3?%zHcq}3WalnN,F#{p:pCNNlnN(lnlnN),r≥2.(r−2)!ϕ(a)p−2p
10、a,pNcq}4WalnN,F#{p:p11、),(a,b)=1,(N−b,a)=1,p+Pr=N}0.771p−1−2r−2>CNNlnN(lnlnN),r≥2.(r−2)!ϕ(a)p−2p
12、a,pN*H3,4Cj'(I)(II)(III)."T)M(KN%(i)kk−1*a=2,b=1.(ii)*a=2(k≥2),bgmodaNxy>N2ZAa(iii)*a=Eskp0,bgmodaNx9b≡N(p0),Dy>
13、)?uwub`YH3,4(I)(II)(III)?ar8DirichletHskH?a2h[A6JkzAd={a:a∈A,d
14、a}.)
15、A
16、AY>skPskz[
17、A
18、∼XIKjAP0b?d,ω(d)(A1)
19、Ad
20、=dX+rd,ω(d)xlk0≤ω(p)