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(2002O08O1608O17,)n,20n+22003n+2002.3n(n),3.,3n,.(1):n=3,?;(2):n.k,k(ab+bc+ca)5(a2+b2+c2)abc,abc.O1O2BC,BCO1.CO1,O2A,AB,O1E,CE,O2F.HAF,HE,O1G,BG,ACD.:AHHF=ACCD.P1,P2,,Pn(n2)1,2,,n.:1P1+P2+1P2+P3++1Pn-2+Pn-1+1Pn-1+Pnn-1n+2.(x,y),xy=yx-y.ABCADBECF.:DEFABC.A1,A2,,A88,l,A1,A2,,A8P1,P2,,P8.8,lPi1,Pi2,,Pi8,,1,2,,8i1,i2,,i8(1,2,1,8,3,7,4,6,5).8,N8=N(A1,A2,,A8),N8.1,2|n.n=2m(mN3),(20m+1)|(2003m+1001).2003m+1001=100(20m+1)+3m+901,(20m+1)|(3m+901).3m+90120m+1=1,2,3,4.,3m+90120m+15,m8969710.m=1,2,,9(20m+1)8(3m+901).n.:,(20m+1)|(2003m+1001).(20m+1,20)=1,(2003m+1001)20-(20m+1)2003=18017,(20m+1)|18017.18017=43419,43419,20m+1=43,419,18017,.,n.(1)n=3,.(91,2,,9):(1,2,3),(1,4,5),(1,6,7),(1,8,9),(2,4,6),(2,7,8),(2,5,9),(3,4,8),(3,5,7),(3,6,9),(4,7,9),(5,6,8).(2),42,3,,3n-1.2|(3n-1).,n.(a-b)2+(b-c)2+(c-a)20,a2+b2+c2ab+bc+ca.k5.k,,k6.112,,k(11+12+12)5(12+12+22),k6.k=6.abc,6(ab+bc+ca)5(a2+b2+c2),5c2-6(a+b)c+5a2+5b2-6ab0.=[6(a+b)]2-45(5a2+5b2-6ab)=64[-(a-b)2+ab]64ab64a+b22=16(a+b)2.,c6(a+b)+106(a+b)+4(a+b)10=a+b.abc.k=6.:abc.ca+b,5a2+5b2+5c2-6ab-6bc-6ca=4(a-b)2+[5c-(a+b)][c-(a+b)]0,6(ab+bc+ca)5(a2+b2+c2).ca+b.:f(x)=5x2-6(a+b)x+5a2+5b2-6ab.f(c)0.f(x)35(a+b),+,f(a+b)=5(a+b)2-6(a+b)(a+b)+5a2+5b2-6ab=4(a-b)20,ca+b.2,BCO1,ACO1C,BEC=FEA=BCA=BCD=90.ABC=,CBD=,AFC=,CEG=.,2AHsinHEA=HEsinHAE,HFsinFEH=HEsinHFE,AHHE=coscos,HFHE=sinsin.AHHF=tantan.RtABC,ACBC=tan;RtBCD,CDBC=tan.ACCD=tantan.AHHF=ACCD.,1P1+P2++1Pn-1+Pn[(P1+P2)++(Pn-1+Pn)](n-1)2.1P1+P2++1Pn-1+Pn(n-1)22(P1++Pn)-P1-Pn(n-1)2n(n+1)-3=(n-1)2(n-1)(n+2)-1(n-1)2(n-1)(n+2)=n-1n+2.x=1,y=1;y=1,x=1;x=y,x=y=1.xy2.1xyy=yx-2y.x2y,y|x.x=ky,k3,kN.,ky=y(k-2)y.k=yk-2.y2,yk-22k-2.2k4k(k5).,k=3,4.k=3,y=3,x=9;k=4,y=2,x=8.,(x,y)(1,1),(9,3),(8,2).:DEAB,AB,,DEsinDAE=AB=c,DE=csinDAE.DCA=90-DAC,,DE=ccosC.5220031,DF=bcosB.,DE+DF=ccosC+bcosB=(2RsinC)cosC+(2RsinB)cosB=R(sin2C+sin2B)=2Rsin(B+C)cos(B-C)=2RsinAcos(B-C)=acos(B-C)a.,DE+EFb,EF+DFc.DE+EF+FD12(a+b+c).:MBC,EEBC,HABC.33,BDHF,1=4.,2=3.1=2,4=3.3=5,4=5,FDE.BCEBCF,EM=FM=12BC.ME=ME,DE+DF=DE+DF=EFMF+ME=BC.,DE+EFAC,EF+FMAB.,.4:DEFABC.DBC,4,DABACD1D2,D1D2ABACEF,DEF.,DEF=DE+EF+FD=D1E+EF+FD2=D1D2.ABACE1F1,DE1F1=DE1+E1F1+F1D=D1E1+E1F1+F1D2D1D2,E1F1EF.,D,DEF.D1AD2=2BAC,AD1=AD=AD2,,D1D2AD,AD,D1D2.,DEFABC,DBCD.5,DEFABC,5ABCDEF,AFE=DFC=CFD2,,EFD2.,D1EF.,DEFABC.ABCMNL,DE+EF+FDMN+NL+LM=12(AB+BC+CA).:,.,A1,A2,,A8.,O.,,.,A1,A2,,A8,,.6Ok.,kC28=28.2k,,l1,l2,,l2k,6.l(l1,,l2k)ljlj+1,ljllj+1.,j,l.l1,,l2kll,j,ljllj+1ljllj+1,j,lljl.ljAj1Aj2,Aj1Ajll,.,2k.,k=C28,,N8=56.(:)62