! " $ % & ' ( ' ( " # " # " ' ! ( # ! ' " ' " ' ' # ( . * ,# - - " ' #- & ) " " & # ) ) " ! " ( . 2 ∞ → ( ) ( )+ 34 λ λ = #& / ( ) λ λ= ' $& # # " 0 11 % ( $ # & ' # " + ! ) . = # =λ# - ( ) = ( ) (λ ) + (λ ) ( ) = = ( 5 & $ λ = 8 - λ = ( )6 # ( ) ( )= =λ9 # " = ( )) =− ( 5 = =# # 4 ( )( ( )# λ =( (λ ) = ( ) = & = ( # = ( )+ 7 (λ ) = ( > # * > & & ( ) = ( ( )) = ( ± ) ( )= = 8 = ( ( :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: % ' 1 ; 0 111 % ! 4 → ( ) + ( ) ⋅ ( ) + ( ) = ( = # = # < ' # . ( ) + ( ) = = # ) ) ( )− = #& ' & & # = ( )( ( )= ( = ' ) # ( ) = ( )= # − ) & # # = = 9/( & ) ) = >) = # - # ( ) #- ( ) + = ' ( )= 6 ( ) ( ) + ( ) # − # # & 9/ # & ( )=± =± ( ( ) = ( ) + # ( )− − 9/ & = 9/ # = # ) - ( $ ( ( #- = # = 9/ #- ( :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: % ' # " $ 11 % ≠ ≠ 1 − = + ( ) "! → − 9 + & − − + → − + + + − = + # = # + =− ( A " $ − # & # − + 8 ! ≠− # ' ' ( )= # - # = ' − ( + # ?@ 4 B − + = ) = − + ( ) ( & ( ) − + ( = − + )( " - & # 8 # − = ⇒ = ( + C # $ 8 & ) -8 # " ( ( )= * '! 8 ' B 4 )( + − ≠− # # ( B #- & ! & # # ) ' 8 ( ' - ' 6 ' & !* " ( :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: ! " # # 7 # " - ' # " * ' ' & ( + & + . - ) = #) & = " - # - $ & # = # & " & & # > # ( )) = ( ( )= + + ( )( # ( )= / ( )) # & + # " # = & #' ' ( . & & -8 # & ( . " ' - ' - " ' = ( & # - & " - " - 8 ( ( )) = ( ( )) = + = - ' & " ' ' ! & " & ' $ ) - " ( # λ# ( 5 & " & & " = # * # 8 ' ' > & # " # & # ! " ( & * " * # ' & ( " # & " & & ' ( 7 ! " & & ! ' ) & ' 0 % - " =λ# - ' $ " #& ' 6 * " & ' # = ( ' & # & B = ( . $ ' " # # * λ( A # + # ( 5 & - ' = & ( " ) * 4 & ≠ - ) ' $ & ( " " * # = + # & # # # = # ' # = #- ' ( = & " % # & - & - 1 ' ??? 4 ; ' 3 # → ( ( )) = ( ( )) + ( ) + ( ) − − < $ ( ( )) + ( ( )) ( )= . = ) ) # & ( ) − ( ( )) + − 6 # ∈ # ( ( )) ( = 4 ( ( ) − ( )) = ( ( )) + ( ) ( ) + ( ( )) − ( ( ) − ( )) = − ( ) ) " ) ' ( >) #) # ( 5 ( )) − ( ) = ( ( )) + ( ) − − & & * =− # & & + − & # - & & # * ( ) ( ) − ( ) = − ) # ' # # # ( ( ) ) = ( ) # ( & $ ( ( ) − ( )) & ! 3 & # & # & " = " ( . ( ) = ( ( ) − ( )) = ( ) − B " " & = ) + − * * - ( ( ( )) # + − ( ( )) − - # ' # = B #- & # ( ) − # = # * ( )− ( * +( ( )− ( )) ( ) − = ( = ( )− ( )) = ( ( )) + ( ) + ( ) − − ( ( )) 5 + ( )+ ( )− -8 " & # ! #' − & - ' ( )= ( 8 ( )= − ( ( :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: $ % # 7 " ' ( > + ' & # # & ( )= < = ( ) = ( )+ ( )# * = 9 ( ( ( )= # # 8 " 8 = # ( )( & ( )= ( )= & # ⋅ & ( )( & # & = ) (− ) = ( ) = − ( ) # ' - = & = ( )6 =− # ! #) & ) = ( )+ ( )( # - ) & ' ( )= = & " ( = # ( ' - 7 2 & 6 & " ' +# − 6 # ( # = " + # ( . * " # #- ! " ( ) = ( ) ( )( # = #= & ( # = 8 ' = # E − = # − =− ( E # − = # ' ) - " # = = ( )) # ' ( ' & ( B ' ( 5 = " ' # = # = # " ' + )= = ( ( )) = ( ( )) = ( ( ) ( )) ( ( )) + ( ( )) = ( ) + ( ) + # " " − =− # ' " ( & # & ( )=( ' = =− # #) =− # > # & & ' #- ' & ( = ( & = - & ' " 9 D = ) ' # 8 # # # " −⋅ ( 8 & ( # +⋅ ' # ' & # ' = # ' & − ' ! 7 # # # & " ( )= " & # ( ( ( ))) = @ ( ) = =( > # ) = ( " ' # & # 8 =F F ! = ' 8 # = - ' % ' # # " # " " # ' # $ - ! # - ' 1 000111 % ?? 4 ' → 5 - ) 5 +( ( + ( )) = - ' # ' # ( )) # ( & & # = ( " 7 < ' # ' # - & ( # " ' # # ' ( G ! = ( " # - & + λ= ( (λ ) = (λ #) + ( )) ∈ ) ( ( )) = = ) = +( +( # ( ( )) = ( ( )) = ( ' −( = 4 ( )) ( +( ( )) =− # ( )) )) = ' ( −( ? = # λ 8 = =λ =λ# 4 ( )) + ( ( )) # * (λ )) = λ + ( (λ )) = ( # λ +( ( )) # = - ( ( λ )) = ' (λ ) = # λ- - #- # = #- = ( > & # ' ' ' #- & ' − # ( ( )= = =− + # & ( ( − ))) = ( − ) + ( & ' ) D > (− ) + ( ) # = ( ( ))) = ( ) + ( ( )) + # = + # - & > # & & " = # = ( . + ( ' + & 4 # # & ( ( ))) = ( ) + ( ( )) − -− = ( )+ ( ) = ( )+ ( )( ' # & ) = − (( − ) + ( − )) = − ( ( − ) + ( − )) = ( ) + ( ) ( ' #= ) > ( G # ' # + = " " ( )= ' # 8 > # & ' # ( )# ≥ = ( - ( . & =− − # - ' # # = # - #) ' ( ( )= ( + ( )) # ' ( < & ( 5 = − . = ! #) ( ) = ( ( )) ( & ' ( = # # ) ' # & = ( < = 8 8 " ! ) = ( 5 > # ( :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: ( ) ' 7 " = ( " " * " & " # - & " ' * ' ) ' ' ) ( " 7 ( ! 1 ?@= 4 * ' # # + = , → % ' →∞ # - = ' 6 = ' " # ' * = # # - ' # # # & ( ( # = # ' & # ( )= # = ( & ( = & = & = " # # = # - & = # ( H " # ' # ( ))) = ( ) ( ) # ' ( # & ) & ' # ) # ( # " # * = ' - & # & & =9 # . = ' # = ( > ' #- & ' # & ' ' - ' ' 001G % >) " - # " - & & # & ' ' = ( E ) - = - " = ( ( G ) & # ) = " # # " = & " = - ( 5 ) . & & ' " * { " # − #- ( − − )=( − " " ( )= = - 9 & * = " - # = ( # = ( # * }# " 8 ! " < ( 5 ) ! ! " & ( ' # # & #- = 9 ( 8 = # & - "! ( ( )) = - = # ) ≠ # ' ( " = # # ' >) ) * ( ) & ( # # ( . " > ( " # " # " & ' ( 5 = 4 = ( )( :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: < ) ' " # ( # # " 1 # - ) ) ! ' 1 & ' ! $ - ; ! - ( 000G % ??/ 4 ' + ! − # + → = + + + , − < < # < #' >) "! + > # = & ( & ( ( )) = ( + $ - ' # ( # + ) -# !* − # ) # $ " #- & = + & = ) & ( )+ ( ) = ( +)= − + + + = + ' # ( )= 6 + & ( - & ( +=− " −# ( −) = −# − − = − 6 − = ( #& + )= . ( ( #- − +( " += ! # ( - & & − + ! − # + )= + + + ' #- +≤ & - " ' 6 = +# " # " − < ≤ # # ' ) & & ( 9 = # − ( . # " # # ' ( 5 & & ( - ) ( C 8 # ( )+ ( )( + ( 7 " & # ( B !* ) = ( " ! % ' & ) ( ) + ( )) = + ( ' # & ( )+ ( ) = = & ' $ = # ) + = # - * # >− # " - ' # ( )) # + + # # + )( − 4 = # ( ) + ( )) = ( ) 6 = # 7 ( )) + ( ) ( ( ( )) − ( ( )) = ( - & # ) + = ' #) ) = ( 7 & - & ( 8 = # 5 −= = −# ! >) −=− & 8 " ' $& ≠ ( 5 + " 8 # ( + = # $ & 4 ( ) + ( )) = ) − − + # ( + + )= = −( + ) * ) = + + ( )+ & ' # 4 - ( )= ( ) ( + # # I − + $ ( ) =− * ' - − =− − + + + ( G " < # # ! & #) ( & ) =− B #& ( ( )=− 8 " ( #& = #- " # −=− " ' ' ( + ) # ' # # $ 9 ( :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: . % % ( " ) " " * $ " ( " # & ( # ! ) * & # & & ' - & ' * & ' 8 & & / " ' ) ( $ # ; 00G11 % ! # 1 ?@3 4 * + # ' + = + ≥ != ≠ ≤ <! # ' & ( )= ( = = − ( )= ( = ) = ( ) ( ( )) = + + ≤ < & ) = ( ) (( ) ( )) # − ( )≥ . ≠ = − −ε# # ( −ε ) = = # =− > # " ( ≥ ( - # > # & # ( + ) = ( ) (( − & − −ε ) & # ( − ) ( )≥ # ( >ε> # & ( )) # − −ε ) ( ( )< # # ( )> − # 6 & " # * δ> & ( )= 5 − +δ ( # ε= & − −ε = #& ( )δ ( ) − ( ; > # # ≤ < # ( )= B & # & ( ( )) ( ) = $ & # − # ( - & = − − − ) = − ) ' # & ' " & #) ( 8 - )( + 6 # ' ( = − − ) & " # # & ( :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: E -' & ' " " + $ ,# ( ' ' ) ' ) ' * & # " #- ! ' ( ' G1 % & # * ! $ & 8 " & # 1 ! = ?? 4 ≤ ≤ & = -$ = * -! − = − /- 00 ' & − = 9= = ! 9= - # 9?≤ ≤@9?# - # = 9/ & ' ( )= = − = 9 ( )= ( 9=≤ ≤ 9=( 9?≤ ≤ 9?# - & ( . & 3 " ==9/ # ' J # K ' # - ! ' ' $ ! " ' * & 2 # ' @9 ?? ' # ) L ! ' ) 9=# 9?# 9 ! ' " 9=# ' ) - ( ( = # = - & = = 39 ?? < 9= 9=< − ' 9=6 & = 9 #- = = − = ⋅ = ( ' ' # & = ) = ! ⋅ ?? ==?@ >=; @==⋅ M) = & # # = # ( ' ) ' # = − 6 6 # 3> ?? ( = − = 6 = − = ( ( :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 1 2 * * " " ' #& & ( 5 " 4 5 ; 0% ! 1 ?3@ 4 # " & * ( )= + ( ) − ( ( )) + 3 4 + = = * ) 5 5 ' 6 9 - $ #& . - ( + ) − ( + )− ( + # # 9 - - ( = + $ & = + )= ( )− ' - & 9 # + ' & # + )− = # " ( ) − ( ( )) ( + " " ( ( )) 6 − @ ' # ( )− & ( )= 6 ( $ 8 + ( )− # & # ( )= ( = − )− = # #) 5 + N# ( - 6 = ( ( )− ' ( 8 # # ( )− + # ( ) − ( ( )) = & # )− )+ + + + # ) − >) ( ' = + − # # ( )+ = ( ) − ( ( )) 6 & ) ) ' $ " - ( B & # # " ( > ( + + )− ( )− ≤ ( 9 - & # & # 9 ≤ & + & ! #) = ( & # & < 9 #& ' ' # + # ( ) 4 " = 9 +F " ' +φ F9 # =π9 - & # & " φ# # + $ ,# = # - ' ( . = 9 - = # + − − # B & # #- & + ) "! = = + + − − = = + # = # = = ( ! # ) !O & # " # $ # ) ) ' - # ) $ ( :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 5 ; & 01G % ! # 7 ? * ( 3 1 + )+ ( )= − 5 ( ) ( ) # 7 7≤ ≤ ? 7≤ ≤ 4 ' ( ( . & * ' - & F F> ( . # ' #& + ( )+ ( − )≥ ( + # - )+ ( − )= ( ) ( )> ( )( ' & $& ' # ) ( . + F=F F ∆> # - & F+∆# " ( + - ( # )+ ( )≥ ( + + ( )+ = ( ( 7 ) # ( +( $ ) ( +( + ) )> ) ( + ( )> ( )+ + & # +( − ∆( ≥ # ) ) +∆≥ ( ) + ∆( = ( . +( − ) )≥ ( = # +( − ( +( + + ) )+ ( ) ( )> ) )> ( ' > 9∆# & + )> ( )+ E + ) ) ( + ) ) +∆ > ( ) +( F F≤ ( B & = # ( ! " " % & '((*** ( " ( & )∆( & 8 % + ∆> + = ( = & # +( − ∆> # * # #- & ) ∆ )− ( + # ' ) ( )> + + ) )+ ( ( ( - - + )+ ( ) = )> ( + ) ' # +& " & '(( &" '(( " " , " (" "& )( # $ & Revista Escolar de la Olimpíada Iberoamericana de Matemática http://www.campus-oei.org/oim/revistaoim/ Edita: