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 %The Van der Waerden conjecture6, speaker:YO W[ Z  ContentsoDefinitions and notations The Van der Waerden conjecture Preparations A proof of the Van der Waerden conjectureP",  Definitions and notations Definitions and notationsRecall:Definitions and notations The Van der Waerden conjecture,    Preparations'Theorem 12.1: Proof: By Theorem 5.4$(  Preparations Def:  Preparations Note:  Preparations Fact:   Preparations  Theorem 12.2:$ Proof of Theorem 12.2 ' Proof of Theorem 12.2  )Proof of Theorem 12.2  +Proof of Theorem 12.2  -Proof of Theorem 12.2  /Proof of Theorem 12.2  0 Preparations  Problem 12A:3 Preparations Corollary (i) of Theorem 12.2:5 Preparations LCorollary (ii) of Theorem 12.2: Proof: By Theorem 12.2 and Problem 12A. "LZZM *7 Preparations  Problem 12B:9 Preparations MTheorem 12.3: Proof: By Larange Multiplier, Theorem 12.2, and Problem 12B.,; Preparations KTheorem 12.4: Proof: By Corollary (ii) of Theorem 12.2 and Theorem 12.3.= Preparations Def:? Preparations  Theorem 12.5:A Preparations  C Preparations 7Theorem 12.6: Proof: By induction and Theorem 12.5.E Preparations Corollary of Theorem 12.6:G Preparations  I Preparations FTheorem 12.7: Proof: By Theorem 12.4 and Corollary of Theorem 12.6.K)A proof of the Van der Waerden conjecture, Substitution Principle:Q )A proof of the Van der Waerden conjecture6   S!)A proof of the Van der Waerden conjecture6   V")A proof of the Van der Waerden conjecture6   W#)A proof of the Van der Waerden conjecture6  1 ` fp=` f3` 33f` 3f33` 3f3f` fff3` f3` 3|f>?" dd@,|?" dd@   " @ ` n?" dd@   @@``PV    @ ` `p>> P-H-`44,(    BW CfDE,F6 W  Pn n /Hf  W W @`""  S  "`P  L cN NN}/kGrjL#j_    C ` "   |0 cN NN}/kGr ,{Nd\ ,{ Nd\ ,{Vd\ ,{Nd\    C  "``  b*0  C  "`   d* 0  C < "`8  d* 0  B_ CwDE,F6  12w  _  `@`"55^  B C DE F*    FRj @`"%wT  i   " iV   BCDE`Fj3R3[J3d =xjXy.|7 sb"3324@`" Y:   BCDEF"x@`" E   B2C5DE0F: 3~25Fy+**. @`",X  BCDE F*ENEE@`"V  BCDE F*$ @`" lE  BCDEF"H@`"C  BCDE F*PWPP@`"  BC\DEF&j\+@`"  B8CDEFN8 @`"[mb  i # " ib   # "   B9CDE(F2 kr $9[CJe kk@`"Z  BC DE$F. 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Waerden conjecture Preparations A proof of the Van der Waerden conjectureP",  Definitions and notations Definitions and notationsRecall:Definitions and notations The Van der Waerden conjecture,    Preparations'Theorem 12.1: Proof: By Theorem 5.4$(  PreparationsDef:  PreparationsNote:  PreparationsFact:   Preparations Theorem 12.2:$ Proof of Theorem 12.2 ' Proof of Theorem 12.2  )Proof of Theorem 12.2  +Proof of Theorem 12.2  -Proof of Theorem 12.2  /Proof of Theorem 12.2  0 Preparations Problem 12A:3 PreparationsCorollary (i) of Theorem 12.2:5 PreparationsLCorollary (ii) of Theorem 12.2: Proof: By Theorem 12.2 and Problem 12A. "LZZM7 Preparations Problem 12B:9 PreparationsMTheorem 12.3: Proof: By Larange Multiplier, Theorem 12.2, and Problem 12B.,; PreparationsKTheorem 12.4: Proof: By Corollary (ii) of Theorem 12.2 and Theorem 12.3.= PreparationsDef:? Preparations Theorem 12.5:A Preparations C Preparations7Theorem 12.6: Proof: By induction and Theorem 12.5.E PreparationsCorollary of Theorem 12.6:G Preparations I PreparationsFTheorem 12.7: Proof: By Theorem 12.4 and Corollary of Theorem 12.6.K)A proof of the Van der Waerden conjecture, Substitution Principle:Q )A proof of the Van der Waerden conjecture,   S!)A proof of the Van der Waerden conjecture,   V")A proof of the Van der Waerden conjecture,   W#)A proof of the Van der Waerden conjecture,  Y$ Thank all ^_^& H}  H$(  Hr H S `P   r H S  I    H H 0޽h ? fp=___PPT10i. O+D=' = @B +rY:$? =Y8(     ՜.+,0P     pùjppekFo$A *Arial sөComic Sans MS WingdingsCrayonsMathType 5.0 EquationThe Van der Waerden conjecture ContentsDefinitions and notationsDefinitions and notationsDefinitions and notationsThe Van der Waerden conjecture Preparations Preparations Preparations Preparations PreparationsProof of Theorem 12.2Proof of Theorem 12.2Proof of Theorem 12.2Proof of Theorem 12.2Proof of Theorem 12.2Proof of Theorem 12.2 Preparations Preparations Preparations Preparations Preparations Preparations Preparations Preparations Preparations Preparations Preparations Preparations Preparations*A proof of the Van der Waerden conjecture*A proof of the Van der Waerden conjecture*A proof of the Van der Waerden conjecture*A proof of the Van der Waerden conjecture*A proof of the Van der Waerden conjecture  ϥΦr ²]pdO OLE A{ vD$_"confishconfish C2$Ҍה,jԕKG2$;xd̟6I4fM2$|"(@i mP2$O_| gXvT2$ys{apfXU!ZX2$mSSNM&K{\2$ѲAE* #o]?w`2$ewr?I6 (AOc2$Fx1uiB g2$P=Oׅ l2$J$g8NrNr2$zI*ui Eu2$NICU `{Uy2$R(׼ΦBX|2$&@P"koMJ2$} sX!M`l2$45@7$2$4*\ Iy`Br 2$?1'{@q(i+j 0AA@8 wR ʚ;;k8ʚ;g4BdBdPz[ 0ppp@ <4dddd| 00<4!d!d| 00 80___PPT10 pp?  %PThe Van der Waerden conjecture6, speaker:YO W[ Z  ContentsoDefinitions and notations The Van der Waerden conjecture Preparations A proof of the Van der Waerden conjectureP",  Definitions and notations Definitions and notationsRecall:Definitions and notations The Van der Waerden conjecture,    Preparations'Theorem 12.1: Proof: By Theorem 5.4$(  PreparationsDef:  PreparationsNote:  PreparationsFact:   Preparations Theorem 12.2:$ Proof of Theorem 12.2 ' Proof of Theorem 12.2  )Proof of Theorem 12.2  +Proof of Theorem 12.2  -Proof of Theorem 12.2  /Proof of Theorem 12.2  0 Preparations Problem 12A:3 PreparationsCorollary (i) of Theorem 12.2:5 PreparationsLCorollary (ii) of Theorem 12.2: Proof: By Theorem 12.2 and Problem 12A. "LZZM7 Preparations Problem 12B:9 PreparationsNTheorem 12.3: Proof: By Lagrange Multiplier, Theorem 12.2, and Problem 12B.; PreparationsKTheorem 12.4: Proof: By Corollary (ii) of Theorem 12.2 and Theorem 12.3.= PreparationsDef:? Preparations Theorem 12.5:A Preparations C Preparations7Theorem 12.6: Proof: By induction and Theorem 12.5.E PreparationsCorollary of Theorem 12.6:G Preparations I PreparationsFTheorem 12.7: Proof: By Theorem 12.4 and Corollary of Theorem 12.6.K)A proof of the Van der Waerden conjecture, Substitution Principle:Q )A proof of the Van der Waerden conjecture,   S!)A proof of the Van der Waerden conjecture,   V")A proof of the Van der Waerden conjecture,   W#)A proof of the Van der Waerden conjecture,  Y$ Thank all ^_^& H  0(  r  S `P   r  S    `  c $A b??"  bH  0޽h ? fp=___PPT10i.O 3+D=' = @B +r=9u? =xY8(    Equation Equation.DSMT40*MathType 5.0 EquationEquation Equation.DSMT40*MathType 5.0 EquationEquation Equation.DSMT40*MathType 5.0 Equation*Equation Equation.DSMT40*MathType 5.0 Equation/Equation Equation.DSMT40*MathType 5.0 EquationEquation Equation.DSMT40*MathType 5.0 Equation:"Equation Equation.DSMT40*MathType 5.0 Equation;#Equation Equation.DSMT40*MathType 5.0 Equation>%Equation Equation.DSMT40*MathType 5.0 EquationN&Equation Equation.DSMT40*MathType 5.0 EquationV(Equation Equation.DSMT40*MathType 5.0 EquationS*Equation Equation.DSMT40*MathType 5.0 EquationZ,Equation Equation.DSMT40*MathType 5.0 Equation[.Equation Equation.DSMT40*MathType 5.0 Equation\1Equation Equation.DSMT40*MathType 5.0 Equation]2Equation Equation.DSMT40*MathType 5.0 Equation`4Equation Equation.DSMT40*MathType 5.0 Equationa6Equation Equation.DSMT40*MathType 5.0 Equationb8Equation Equation.DSMT40*MathType 5.0 Equationc:Equation Equation.DSMT40*MathType 5.0 Equationi<Equation Equation.DSMT40*MathType 5.0 Equationk>Equation Equation.DSMT40*MathType 5.0 Equationn@Equation Equation.DSMT40*MathType 5.0 EquationoBEquation Equation.DSMT40*MathType 5.0 EquationtDEquation Equation.DSMT40*MathType 5.0 EquationwFEquation Equation.DSMT40*MathType 5.0 EquationxHEquation Equation.DSMT40*MathType 5.0 EquationyJEquation Equation.DSMT40*MathType 5.0 Equation~LEquation Equation.DSMT40*MathType 5.0 EquationMEquation Equation.DSMT40*MathType 5.0 EquationNEquation Equation.DSMT40*MathType 5.0 EquationOEquation Equation.DSMT40*MathType 5.0 EquationPEquation Equation.DSMT40*MathType 5.0 EquationREquation Equation.DSMT40*MathType 5.0 EquationTEquation Equation.DSMT40*MathType 5.0 EquationUEquation Equation.DSMT40*MathType 5.0 EquationXEquation Equation.DSMT40*MathType 5.0 Equation/ 00DArialngs08 08z[ 00De0}fԚngs08 08z[ 00 DComic Sans MS08 08z[ 00B0DWingdings MS08 08z[ 00 A .  @n?" dd@  @@``   HS&** 5 >>&5'( 01 2345679:;<=>?@ABCDEFGHIJKLMNOPQo2$-󍒁ŧRrr12$j5Pٚ + E2$COtqVB2$CCn"Zd_ 2$τҏABB2$mǾzA ci2$Je:?Y9;Bf2$12$$G`^4;42$p>+)5S4g62$@[(լث)Y;2$їeǏ7 ?f9@@2$1lBH9CSi6hvm C2$Ҍה,jԕKG2$;xd̟6I4fM2$|"(@i mP2$O_| gXvT2$ys{apfXU!ZX2$mSSNM&K{\2$ѲAE* #o]?w`2$ewr?I6 (AOc2$Fx1uiB g2$P=Oׅ l2$J$g8NrNr2$zI*ui Eu2$NICU `{Uy2$R(׼ΦBX|2$&@P"koMJ2$} sX!M`l2$45@7$2$4*\ Iy`Br 2$?1'{@q(i+j 0AA@8 wR ʚ;;k8ʚ;g4BdBdPz[ 0ppp@ <4dddd| 00<4!d!d| 00 80___PPT10 pp?  %PThe Van der Waerden conjecture6, speaker:YO W[ Z  ContentsoDefinitions and notations The Van der Waerden conjecture Preparations A proof of the Van der Waerden conjectureP",  Definitions and notations Definitions and notationsRecall:Definitions and notations The Van der Waerden conjecture,    Preparations'Theorem 12.1: Proof: By Theorem 5.4$(  PreparationsDef:  PreparationsNote:  PreparationsFact:   Preparations Theorem 12.2:$ Proof of Theorem 12.2 ' Proof of Theorem 12.2  )Proof of Theorem 12.2  +Proof of Theorem 12.2  -Proof of Theorem 12.2  /Proof of Theorem 12.2  0 Preparations Problem 12A:3 PreparationsCorollary (i) of Theorem 12.2:5 PreparationsLCorollary (ii) of Theorem 12.2: Proof: By Theorem 12.2 and Problem 12A. "LZZM7 Preparations Problem 12B:9 PreparationsNTheorem 12.3: Proof: By Lagrange Multiplier, Theorem 12.2, and Problem 12B.; PreparationsKTheorem 12.4: Proof: By Corollary (ii) of Theorem 12.2 and Theorem 12.3.= PreparationsDef:? Preparations Theorem 12.5:A Preparations C Preparations7Theorem 12.6: Proof: By induction and Theorem 12.5.E PreparationsCorollary of Theorem 12.6:G Preparations I PreparationsFTheorem 12.7: Proof: By Theorem 12.4 and Corollary of Theorem 12.6.K)A proof of the Van der Waerden conjecture, Substitution Principle:Q )A proof of the Van der Waerden conjecture,   S!)A proof of the Van der Waerden conjecture,   V")A proof of the Van der Waerden conjecture,   W#)A proof of the Van der Waerden conjecture,  Y$ Thank all ^_^& Hrx#? xY