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2001(2001204215)(40,8)1.x12001-xx-1=12001.x3-2001x4+29=.12.1,ABCD64,CEFG36,DFBGO.DBO.3.a2+b2=6abab0.a+ba-b=.4.6+a-3131+a3-17160a-3131+a3-171604,.25.1ABC,P0BC,P0P1CAP1,P1P2ABP2,P2P3BCP3.P3P0,P1P2P3.(15):a4+b4+(a+b)4=2(a2+ab+b2)2.(15)123456,,,16,,.:.(15)2,ABC,ABD,CAE,DE,AD=BC=CE=DE.:BAC=100.(15)10,101,10101,1010101,101010101,,?.1.-692.248373.24.6255.312a4+b4+(a+b)4-2(a2+ab+b2)2=(a2+b2)2-2a2b2+(a2+2ab+b2)2-2(a2+ab+b2)2=[(a2+b2)2-(a2+ab+b2)2]+[(a2+2ab+b2)2-(a2+ab+b2)2]-2a2b2=(2a2+2b2+ab)(-ab)+(2a2+3ab+2b2)ab-2a2b2=ab(-2a2-2b2-ab+2a2+3ab+2b2-2ab)=0.a1a2a3a4a5a6;b1b2b3b4b5b6.(ai,bi1,2,3,4,5,6.i=1,2,3,4,5,6.)|a1-b1||a2-b2||a3-b3||a4-b4||a5-b5||a6-b6|.,012345.,6i=1|ai-bi|=0+1+2+3+4+5=15(1).,|ai-bi|ai-bi(i=1,2,3,4,5,6),,82©1994-2007ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.=1|ai-bi|6i=1(ai-bi)=(a1+a2+a3+a4+a5+a6)-(b1+b2+b3+b4+b5+b6)=(1+2+3+4+5+6)-(1+2+3+4+5+6)=0,,(1).|a1-b1||a2-b2||a3-b3||a4-b4||a5-b5||a6-b6|.ADE,EAD,ABC,BAC,,ABAC,AB=AC.33,CADCF,DBCF,EF,BCFD.,DB=CF,BC=DF,EAD=ECF.ADECEF,AD=CE,AE=DB=CF,EAD=ECF,ADECEF,ED=EF.ED=BC=DF,DEF,,EDF=60.BAC=,ADF=ABC=180-2,DAE=180-,ADE=180-2DAE=180-2(180-)=2-180.ADF+ADE=EDF=60,180-2+(2-180)=60.=100,BAC=100.,101.,N=10101001k1(k3)(k-10).11N=111010101k1=1111112k1=1111k1(10k+1).(1)k3,11111111k1,,11|(10k+1),10k+111=M11.N=1111k110k+111=1111k1M1.N.(2)k3,11|1111k1.111111k1=M21.N=111111k1(10k+1)=M2(10k+1).N.,k3,N=1010101k1.,101,10101,1010101,101010101,,101.():2519:2518,()(1,12,3)(20%):,:100037:0102689024869220024©1994-2007ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.