搜索
2007IMOABO,MAB,CO,COCSCT,MSMTABEF.EFAB,OSOTXY.CO,OPQ,MPABR,ZPQR.:XYZ.()x:x=pq1,,pq,N,nN,|{xn}-|12(p+q),,{a}a..()10C63,9S.S.()f:Q+Q+,f(x)+f(y)+2xyf(xy)=f(xy)f(x+y),,Q+.()x1,x2,,xnn(n2),A=|ni=1xi|0,B=max1ijn|xj-xi|0.:n1,2,,n,1,2,,nk1,k2,,kn,|ni=1xkii|AB2A+Bmax1in|i|.()n,AA{1,2,,n},An.:|A|119n+5.()1,OM.XESOMS,,XES.XXEXS,ABCS.1PQR,MAMC.MRMP=MA2=MEMS.CQCP=CS2.,MCZX.,MC.,ZXMC.,ZYMC.,XYZ.,1.1.mn=[xn+1]-[xn].nN,|(x-1)xn-mn|=|{xn+1}-{xn}||{xn+1}-|+|{xn}-|1p+q.m+1,5-rm.,9C2r(m+1)2+C1rC15-r(m+1)m+C25-rm2=10m2+4rm+12r(r-1).310CnM,n=6m+r(mr,0r6).M9Sn.Sn20m3+10rm2+2r(r-1)m+16r(r-1)(r-2).3:n.n=12,Sn=0,.n=k(k2),,k=6m+r(mr,0r6),Sk20m3+10rm2+2r(r-1)m+16r(r-1)(r-2).2,910m2+4rm+12r(r-1)(r=5,2,10(m+1)2,),9,PSP=10m2+4rm+12r(r-1).P,k=6m+r.k,9Sk,Sk20m3+10rm2+2r(r-1)m+16r(r-1)(r-2).Sk+1=Sk+SP20m3+10rm2+2r(r-1)m+16r(r-1)(r-2)+10m2+4rm+12r(r-1)=20m3+10(r+1)m2+2(r+1)rm+16r(r+1)(r-1).,n=k+1=6m+(r+1),.,r=5,m=k+1=6(m+1),Sk+1=20(m+1)3,..n=63=610+3,3S20103+103102+23210+16321=23121.Smax=23121.(1):f(1)=1.,,y=1,f(1)=a,f(x)+a+2xf(x)=f(x)f(x+1),f(x+1)=f(x)(1+2x)f(x)+a.f(2)=a4a=14,f(3)=15+4a,f(4)=17+5a+4a2.,x=y=2,2f(2)+8f(4)=f(4)f(4)=1.,12+87+5a+4a2=1.a=1.(2):f(x+n)=f(x)(n2+2nx)f(x)+1(n=1,2,).f(x+1)=f(x)(1+2x)f(x)+1.f(x+k)=f(x)(k2+2kx)f(x)+1,f(x+k+1)=f(x+k)[1+2(x+k)]f(x+k)+1=f(x)[(k+1)2+2(k+1)x]f(x)+1.x=1,f(1)=1,f(1+n)=1n2+2n+1=1(n+1)2,f(n)=1n2(n=1,2,).(3):f1n=n2=11n22(n=1,2,).,x=1n,fn+1n=f1n(n2+2)f1n+1.,y=1x,f(x)+f1x+2=1fx+1x.,f(n)+f1n+2=1fn+1n=n2+2+1f1n]1n2+f1n=n2+1f1n]f21n+1n2-n2f1n-1=0]f1n-n2f1n+1n2=0.,f(1n)=n2=11n2.(4):q=nm,(n,m)=1,f(q)=1q2.mn,(n,m)=1.x=n,y=1m,f1m+f(n)+2nmfnm=fnmfn+1m.x=1m,fn+1m=f1mn2+2nmf1m+1=1n2+2nm+1m2.,1n2+m2+2nmfnm=n+1m2fnm,1n2+m2=n2+1m2fnm.,f(q)=fnm=1n2+m2n2+1m2=mn2=1q2.,f(x)=1x2.,f(x)=1x2.f(x)=1x2.|k|=max1in|i|(k{1,2,,n}).:max(k1,k2,,kn)Sn|ni=1xkii|AB2A+B|k|,,Sn1,2,,n.|xn-x1|=max1ijn|xj-xi|=B,|n-1|=max1ijn|j-i|.,1=x11+x22++xn-1n-1+xnn,2=xn1+x22++xn-1n-1+x1n.max(k1,k2,,kn)Sn|ni=1xkii|max{|1|,|2|}12(|1|+|2|)12|2-1|=12|x1n+xn1-x11-xnn|=12|xn-x1||n-1|=12B|n-1|.|n-1|=x|k|.0x2.,max(k1,k2,,kn)Sn|ni=1xkii|12Bx|k|.,n1=x11+x22++xn-1n-1+xnn,2=x21+x32++xnn-1+x1n,n=xn1+x12++xn-2n-1+xn-1n.max(k1,k2,,kn)Sn|ni=1xkii|max1in|i|1nni=1|i|1n|ni=1i|=An|ni=1i|=An|nk-jk(k-j)|An(n|k|-jk|k-j|)An[n|k|-(n-1)|n-1|]=An[n|k|-(n-1)x|k|]=A1-n-1nx|k|.max(k1,k2,,kn)Sn|ni=1xkii|maxBx2,A1-n-1nx|k|Bx2An-1n+A1-n-1nxB2An-1n+B2|k|=AB2A+B-2An|k|AB2A+B|k|.a(n,2n],[a,a+1]=a(a+1)n.|A(n,2n]|12(2-1)n+1.a(2n,3n],[a,a+1]=a(a+1)n,[a+1,a+2]=(a+1)(a+2)n,[a,a+2]12a(a+2)n.|A(2n,3n]|13(3-2)n+1.,|A(3n,2n]|14(4-3)n+1.|A[1,2n]|n+12(2-1)n+13(3-2)n+14(4-3)n+3=1+26+312n+3.k,abnk+1,nk(ab),[a,b]=as=bt.a(a,b)s=b(a,b)t.a(a,b)b(a,b),sb(a,b).,[a,b]=asab(a,b)aba-b=b+b2a-bnk+1+nk+12nk-nk+1=n.|Ank+1,nk|1.T,nT+12nnT,|A(2n,n]|Tk=1|Ank+1,nk|Tn2.|A|32+26+312n+3119n+5.()(100)(7,42)11.1,,y=ax2+mc(a0)ABOCABC,ac=-2.m().(A)1(B)-1(C)2(D)-22.16(),y=x2+mx+n.y=x2+mx+nx().(A)512(B)49(C)1736(D)123.,(4=22-02,12=42-22,20=62-42).,().2008;;;1100100,13.(A)1(B)2(C)3(D)44.ABC,AB=AC=b,BC=a.