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{SECT 0 {EXCHG {PARA 262 "" 0 "" {TEXT -1 23 "TP 4 - DO OD -  CORRIGE
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 1 "1" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 42 "u:= 0 :n:=10: for k to n do u :=u+k od :u;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#b" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 52 "Si la valeur de u au sortir de la k-i\350me boucle est " }
{XPPEDIT 18 0 "u[k];" "6#&%\"uG6#%\"kG" }{TEXT -1 34 " on a la relatio
n de r\351currence : " }{XPPEDIT 18 0 "u[k] = u[k-1]+k;" "6#/&%\"uG6#%
\"kG,&&F%6#,&F'\"\"\"F,!\"\"F,F'F," }{TEXT -1 4 " :  " }{XPPEDIT 18 0 
"u[n];" "6#&%\"uG6#%\"nG" }{TEXT -1 40 " est donc \351gal \340 1+2+...
+n (= n(n+1)/2)." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "u:= 0 :
n:=10: for k to 2*n+1 by 2 do u :=u+k od :u;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"#b" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 50 "Si la vale
ur de u au sortir de la boucle d'indice " }{TEXT 260 1 "k" }{TEXT -1 
5 " est " }{XPPEDIT 18 0 "u[k];" "6#&%\"uG6#%\"kG" }{TEXT -1 33 " on a
 la relation de r\351currence :" }{XPPEDIT 18 0 "u[k] = u[k-2]+k;" "6#
/&%\"uG6#%\"kG,&&F%6#,&F'\"\"\"\"\"#!\"\"F,F'F," }{TEXT -1 4 " :  " }
{XPPEDIT 18 0 "u[2*n-1];" "6#&%\"uG6#,&*&\"\"#\"\"\"%\"nGF)F)F)!\"\"" 
}{TEXT -1 33 " est donc \351gal \340 1+3+...+2n-1 (= " }{XPPEDIT 18 0 
"n^2;" "6#*$%\"nG\"\"#" }{TEXT -1 3 " )." }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "u := 1 : fo
r k to n do u :=u*k od :u;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"(+)GO
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 52 "Si la valeur de u au sortir d
e la k-i\350me boucle est " }{XPPEDIT 18 0 "u[k];" "6#&%\"uG6#%\"kG" }
{TEXT -1 34 " on a la relation de r\351currence : " }{XPPEDIT 18 0 "u[
k] = u[k-1].k;" "6#/&%\"uG6#%\"kG-%\".G6$&F%6#,&F'\"\"\"F.!\"\"F'" }
{TEXT -1 5 "  :  " }{XPPEDIT 18 0 "u[n];" "6#&%\"uG6#%\"nG" }{TEXT -1 
32 " est donc \351gal \340 1.2.....n = n!." }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "A := [seq(i
thprime(k),k=1..10)]: u:=0: for k in A do u:=u+k od :u;" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#\"$H\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 52 "S
i la valeur de u au sortir de la k-i\350me boucle est " }{XPPEDIT 18 
0 "u[k];" "6#&%\"uG6#%\"kG" }{TEXT -1 34 " on a la relation de r\351cu
rrence : " }{XPPEDIT 18 0 "u[k] = u[k-1]+p[k];" "6#/&%\"uG6#%\"kG,&&F%
6#,&F'\"\"\"F,!\"\"F,&%\"pG6#F'F," }{TEXT -1 5 "  :  " }{XPPEDIT 18 0 
"u[n];" "6#&%\"uG6#%\"nG" }{TEXT -1 30 " est donc \351gal \340 la somm
e des " }{TEXT 261 1 "n" }{TEXT -1 27 " premiers nombres premiers." }}
}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 32 "u:= 1 :   to n do u :=a*u od :u;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#*$)%\"aG\"#5\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
52 "Si la valeur de u au sortir de la k-i\350me boucle est " }
{XPPEDIT 18 0 "u[k];" "6#&%\"uG6#%\"kG" }{TEXT -1 34 " on a la relatio
n de r\351currence : " }{XPPEDIT 18 0 "u[k] = au[k-1];" "6#/&%\"uG6#%
\"kG&%#auG6#,&F'\"\"\"F,!\"\"" }{TEXT -1 5 "  :  " }{XPPEDIT 18 0 "u[n
];" "6#&%\"uG6#%\"nG" }{TEXT -1 23 " est donc \351gal \340  a^n.." }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 55 "for u while not(is(root(u^3+24,10),integer)) do  od ;
u;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#5" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 119 "On cherche ici les cubes qui, augment\351s de 24, vont d
onner une puissance dixi\350me exacte ; r\351sultat : 10^3 + 24 = 2^10
.\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 27 "2. Coefficients binomiaux.
\n" }{MPLTEXT 1 0 68 "n:=100:p:=50:c:=1:for k to p do c:=c*(n-k+1)/k o
d:c;c-binomial(n,p);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"?cs\\7[L$>kb
aW8*35" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "3. Calcul de
 e." }}{PARA 0 "" 0 "" {TEXT -1 16 "M\351thode \"b\352te\" :" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 94 "Digits:=50:n:=1000:e:=1:t:=time():for k t
o n do e:=e+1/k! od:time()-t;evalf(e);evalf(exp(1));\n" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#$\"&1>#!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"
S+q$4Zsv(\\iENruGg`BX!f%G=G=F!#\\" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$
\"S+q$4Zsv(\\iENruGg`BX!f%G=G=F!#\\" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 53 "M\351thode avec calcul de la factorielle en temps r\351el :" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "n:=1000:e:=0:u:=1:t:=time()
:for k to n do e:=e+1/u : u:=k*u od:time()-t;evalf(e);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#$\"&41#!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"
S+q$4Zsv(\\iENruGg`BX!f%G=G=F!#\\" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
17 "M\351thode de Horner" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 
"n:=1000:e:=1:t:=time():for k from n to 1 by -1 do e:=e/k +1 od:time()
-t;evalf(e);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"$G$!\"$" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#$\"S+q$4Zsv(\\iENruGg`BX!f%G=G=F!#\\" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 260 "" 0 "" 
{TEXT 257 15 "4. Evidemment, " }{XPPEDIT 19 1 "u[n]=1/3" "6#/&%\"uG6#%
\"nG*&\"\"\"F)\"\"$!\"\"" }{TEXT 259 21 "  pour tout n, mais :" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "Digits:=10:u:=1./3 : for n t
o 10 do  u:=-2*u+1  od :u; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+#*H
LLL!#5" }}}{EXCHG {PARA 260 "" 0 "" {TEXT 258 109 "Ceci provient de ce
 que 1./3 n'est pas 1/3 et que la suite (u(n)) diverge d\350s que u(0)
 est diff\351rent de 1/3.\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 22 "5.
 Suite de Fibonacci." }}{PARA 0 "" 0 "" {TEXT -1 17 "version fausse : \+
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "n:=5:F:=0:G:=1: to n do
 print(F,G) :F:=G : G:=F+G   od:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"
\"!\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"\"\"\"#" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6$\"\"#\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"
\"%\"\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\")\"#;" }}}{PARA 0 "" 
0 "" {TEXT -1 76 "En effet, une fois que F a \351t\351 modifi\351e, el
le a perdu sa valeur ant\351rieure !" }}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 35 "version correcte avec des couples :" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 55 "n:=5:F:=0:G:=1: to n do print(F,G) :(F,G):= (G,F+G)
 od:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"!\"\"\"" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6$\"\"\"F#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"\"\"
\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"#\"\"$" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6$\"\"$\"\"&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 108 "b) Une parade sans utiliser les c
ouples : introduire une variable auxiliaire F1 qui conserve la valeur \+
de F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "n:=4:F:=0:G:=1: to
 n do print(F,G): F1:=F: F:=G : G:=F1+G od:" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6$\"\"!\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"\"F#
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"\"\"\"#" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6$\"\"#\"\"$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 11 "Vari
antes :" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 51 "1 ) (Coldefy  2003,  B
enoit-Madin et Chapuis  2004)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 55 "n:=4:F:=0:G:=1: to n do print(F,G): F:=F+G : G:=F+G od:" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"!\"\"\"" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6$\"\"\"\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"$\"
\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\")\"#8" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 28 "2 )  Idem avec des couples :" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 54 "n:=4:F:=0:G:=1: to n do print(F,G): F,G:=F+G,
F+2*G od:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"!\"\"\"" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6$\"\"\"\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$
\"\"$\"\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\")\"#8" }}}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 19 "3)  (Qu\351
ant  2003 )" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "n:=4:F:=0:G:
=1: to n do print(F,G): F:=G-F : G:=F+G od:" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6$\"\"!\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"\"\"
\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"\"\"\"$" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6$\"\"#\"\"&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 16 "4)
  (Hariz 2004)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "n:=4:F:=0
:G:=1:H:=1: to n do print(F,G,H): F:=G: G:=H : H:=F+G:  od:" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6%\"\"!\"\"\"F$" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6%\"\"\"F#\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"\"\"\"#\"\"
$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"#\"\"$\"\"&" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 2 "d)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 
"n:=5:u:=0:v:=1:w:=2: to n do print(u,v,w): u,v,w:=v,w,2*w+u:  od:" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"!\"\"\"\"\"#" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6%\"\"\"\"\"#\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"
\"#\"\"%\"\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"%\"\"*\"#?" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"*\"#?\"#W" }}}{EXCHG {PARA 0 "" 0 
"" {TEXT -1 26 "6. Polyn\364mes de Tchebychev" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 80 "n:=3:T:=1:U:=cos(t):to n do print(T):T1:=T:T:=U:
U:=expand(2*cos(t)*U-T1) od:T;U;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"
\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$cosG6#%\"tG" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#,&*&\"\"#\"\"\")-%$cosG6#%\"tGF%F&F&F&!\"\"" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&\"\"%\"\"\")-%$cosG6#%\"tG\"\"$F&F
&*&F,F&F(F&!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*&\"\")\"\"\")-%
$cosG6#%\"tG\"\"%F&F&*&F%F&)F(\"\"#F&!\"\"F&F&" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 31 "7. Nom
bres compos\351s cons\351cutifs" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 139 "N:=100:p:=2: \nwhile nextprime(p)-p<=N do p:=nextprime(p) od:
\nprintf(`Premi\350re suite de %a compos\351s cons\351cutifs : de %a \+
\340 %a `,N,p+1,p+N): \n" }}{PARA 6 "" 1 "" {TEXT -1 64 "Premi\350re s
uite de 100 compos\351s cons\351cutifs : de 370262 \340 370361 " }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 34 "8. Moyenne arithm\351tico-g\351om\351trique" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 160 "n:=50:e:=10^(-n):Digits:=n+5: u:=1. :v:=2.
:\nfor k from 0 while v-u>e do uu:=u;u:=sqrt(u*v);v:=(uu+v)/2  od :\n`
moyenne arithm\351tico-g\351om\351trique` = evalf(u,n+1);k;" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#/%@moyenne~arithm|dytico-g|dyom|dytriqueG$\"
TJ@K%R'Q(\\(>3lKQKk=po!p/J5zc9!#]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
\"\"'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 63 "Conclusion : en 6 coups,
 on obtient d\351j\340 50 d\351cimales exactes !" }}{PARA 0 "" 0 "" 
{TEXT -1 85 "Remarquons que si l'on fait l'erreur suivante (qui donne \+
l'algorithme de Borchardt) :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 160 "n:=50:e:=10^(-n):Digits:=n+5: u:=1. :v:=2.:\nfor k from 0 while
 v-u>e do u:=sqrt(u*v);v:=(u+v)/2  od :\n`fausse moyenne arithm\351tic
o-g\351om\351trique` = evalf(u,n+1);k;" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#/%Gfausse~moyenne~arithm|dytico-g|dyom|dytriqueG$\"T#>['evDp=vt7
Gj8*G\\Ta*[MKcXg\"!#]" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#%)" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 65 "La convergence est bien plus lente
 : sauriez-vous dire pourquoi ?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 22 "9. Ann\351es avec 3 z\351ros" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 194 "S:=NULL:mini:=1500: maxi:= 2500: \nfor b from 2 to
 maxi/3 \n     do for a from ceil(mini/b^3) to min(maxi/b^3,b-1) \n   \+
        do printf(`l'ann\351e %a s'\351crit %a000 en base %a\\n`, a*b^
3,a,b) od od; " }}{PARA 6 "" 1 "" {TEXT -1 35 "l'ann\351e 1715 s'\351c
rit 5000 en base 7" }}{PARA 6 "" 1 "" {TEXT -1 35 "l'ann\351e 2058 s'
\351crit 6000 en base 7" }}{PARA 6 "" 1 "" {TEXT -1 35 "l'ann\351e 153
6 s'\351crit 3000 en base 8" }}{PARA 6 "" 1 "" {TEXT -1 35 "l'ann\351e
 2048 s'\351crit 4000 en base 8" }}{PARA 6 "" 1 "" {TEXT -1 35 "l'ann
\351e 2187 s'\351crit 3000 en base 9" }}{PARA 6 "" 1 "" {TEXT -1 36 "l
'ann\351e 2000 s'\351crit 2000 en base 10" }}{PARA 6 "" 1 "" {TEXT -1 
36 "l'ann\351e 1728 s'\351crit 1000 en base 12" }}{PARA 6 "" 1 "" 
{TEXT -1 36 "l'ann\351e 2197 s'\351crit 1000 en base 13" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 26 "Avec 4 z\351ros, on obtient :" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 195 "S:=NULL:mini:=1500: maxi:= 2500: \+
\nfor b from 2 to maxi/3 \n     do for a from ceil(mini/b^4) to min(ma
xi/b^4,b-1) \n           do printf(`l'ann\351e %a s'\351crit %a0000 en
 base %a\\n`, a*b^4,a,b) od od; " }}{PARA 6 "" 1 "" {TEXT -1 36 "l'ann
\351e 1875 s'\351crit 30000 en base 5" }}{PARA 6 "" 1 "" {TEXT -1 36 "
l'ann\351e 2500 s'\351crit 40000 en base 5" }}{PARA 6 "" 1 "" {TEXT 
-1 36 "l'ann\351e 2401 s'\351crit 10000 en base 7" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 101 "A votre avis, y a
ura t il en l'an 4000 en base 8 (= 2048) une f\352te similaire \340 ce
lle de l'an 2000 ???" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 23 "10. trian
gle de Pascal." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 157 "n:=5:C:=
array(0..n,-1..n):C[0,0]:=1:for i from 0 to n-1 do C[i,i+1]:=0 :C[i,-1
]:=0 od:\nfor i to n do for j from 0 to i do  C[i,j]:=C[i-1,j]+C[i-1,j
-1] od od:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "for i from 0 to n do \+
 print(seq(C[i,j],j=0..i)) od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"
\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"\"F#" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6%\"\"\"\"\"#F#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&\"\"\"
\"\"$F$F#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'\"\"\"\"\"%\"\"'F$F#" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6(\"\"\"\"\"&\"#5F%F$F#" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0 0" 14 }{VIEWOPTS 1 
1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }