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{EXCHG {PARA 261 "" 0 "" {TEXT -1 7 "RAPPELS" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 55 "f:=2*x+4; g:=x^2+3*x-1; h:= f*4 +g^2;hy:=y*f+(y^
2+1)*g;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG,&%\"xG\"\"#\"\"%\"\"
\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gG,(*$%\"xG\"\"#\"\"\"F'\"\"
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\"*$,(*$F&\"\"#F)F&\"\"$!\"\"F)F-F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#>%#hyG,&*&%\"yG\"\"\",&%\"xG\"\"#\"\"%F(F(F(*&,&*$F'F+F(F(F(F(,(*$F*F
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=expand(h);expand(hy);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"kG,,%\"x
G\"\"#\"#<\"\"\"*$F&\"\"%F)*$F&\"\"$\"\"'*$F&F'\"\"(" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#,2*&%\"yG\"\"\"%\"xGF&\"\"#F%\"\"%*&F%F(F'F(F&*&F%F(
F'F&\"\"$*$F%F(!\"\"*$F'F(F&F'F,F.F&" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 61 "sort(k);collect(hy,x);collect(hy,y,factor);collect(hy
,[x,y]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,,*$%\"xG\"\"%\"\"\"*$F%\"
\"$\"\"'*$F%\"\"#\"\"(F%F,\"#<F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,,
*&,&*$%\"yG\"\"#\"\"\"F)F)F)%\"xGF(F)*&,(F'F(F&\"\"$F-F)F)F*F)F)F'\"\"
%F&!\"\"F/F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,,*&,(*$%\"xG\"\"#\"\"
\"F'\"\"$!\"\"F)F)%\"yGF(F)*&F,F),&F'F(\"\"%F)F)F)F&F)F'F*F+F)" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,,*&,&*$%\"yG\"\"#\"\"\"F)F)F)%\"xGF(F
)*&,(F'F(F&\"\"$F-F)F)F*F)F)F'\"\"%F&!\"\"F/F)" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 122 "indets(hy);coeff(k,x,3);lcoeff(k,x);tcoeff(k-
17,x); # atteindre diff\351rents coefficients l pour leading et t pour
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11 "" 1 "" {XPPMATH 20 "6#\"\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"
\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}}{EXCHG {PARA 260 "" 
0 "" {TEXT -1 36 "Petit retour sur des calculs formels" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "restart; f:= x^8 -1;factor(f); " }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG,&*$%\"xG\"\")\"\"\"!\"\"F)" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#**,&%\"xG\"\"\"!\"\"F&F&,&F%F&F&F&F&,&
*$F%\"\"#F&F&F&F&,&*$F%\"\"%F&F&F&F&" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 35 "alias(a=RootOf(x^4+1));factor(f,a);" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6$%\"IG%\"aG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*2,&
%\"xG\"\"\"*$%\"aG\"\"#F'F',&F&!\"\"F(F'F',&F&F'F)F'F',&F&F,*$F)\"\"$F
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "g:=a^3+1;#on peut faire des calculs
 formels avec a " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gG,&*$%\"aG\"
\"$\"\"\"F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 105 "allvalues
(g);# retourne la suite des valeurs prises par g lorsque a dcrit l'ens
emble des racines de x^4+1" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&,&*$,&*$
\"\"##\"\"\"F'F(*&%\"IGF)F'F(F(\"\"$F)F)F),&*$,&F&#!\"\"F'F*F0F,F)F)F)
,&*$,&F&F(F*F0F,F)F)F),&*$,&F&F0F*F(F,F)F)F)" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 35 "alias(b=RootOf(x^2+1));factor(f,b);" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6%%\"IG%\"aG%\"bG" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#*.,&*$%\"xG\"\"#\"\"\"%\"bG!\"\"F(,&F%F(F)F(F(,&F&F(F)F*F(,&F&F(
F)F(F(,&F&F(F*F(F(,&F&F(F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 60 "factor(f,\{a,b\});# le polynome x^4+1 n'est pas irrductible ..
" }}{PARA 8 "" 1 "" {TEXT -1 158 "Error, (in evala) reducible RootOf d
etected.  Substitutions are, \{RootOf(_Z^4+1) = RootOf(-RootOf(_Z^2+1)
+_Z^2), RootOf(_Z^4+1) = RootOf(_Z^2+RootOf(_Z^2+1))\}" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "factor(f, \{b,sqrt(b)\});# RootOf e
t sqrt sont incompatibles ...." }}{PARA 8 "" 1 "" {TEXT -1 106 "Error,
 (in factor) 2nd argument is not a valid algebraic extension, \{RootOf
(_Z^2+1), RootOf(_Z^2+1)^(1/2)\}" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 42 "restart;h:=x^4+x^3+ x^2 + x+1; irreduc(h);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"hG,,*$%\"xG\"\"%\"\"\"*$F'\"\"$F)*$F'\"
\"#F)F'F)F)F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "irreduc(h,sqrt(5));" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#%&falseG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
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0F*F0F0#F,\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "nops(\");
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "
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\"pG,**$%\"xG\"\"#F(F'\"\"\"*&\"\"&#F)F(F'F)F)F(F)" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 13 "rr:=solve(p);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%#rrG6$,(#!\"\"\"\"%\"\"\"*$\"\"&#F*\"\"#F'*$,&!#5F*F+F.F-#F*F)
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tor(hh,rr[1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(#!\"\"\"\"%\"\"\"*
$\"\"&#F'\"\"#F$*$,&!#5F'F(F+F*#F'F&" }}{PARA 8 "" 1 "" {TEXT -1 110 "
Error, (in factor) 2nd argument is not a valid algebraic extension, -1
/4-1/4*5^(1/2)+1/4*(-10+2*5^(1/2))^(1/2)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 52 "alias(d= RootOf(2*x^2+x-5^(1/2)*x+2)); factor(hh,d);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%\"IG%\"dG" }}{PARA 8 "" 1 "" 
{TEXT -1 99 "Error, (in factor) 2nd argument is not a valid algebraic \+
extension, RootOf(2*_Z^2+(1-5^(1/2))*_Z+2)" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 44 "alias(e=RootOf(x^2 =5)); convert(hh,RootOf);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6%%\"IG%\"dG%\"eG" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,$*&,**$%\"xG\"\"#!\"#F'!\"\"*&%\"eG\"\"\"F'F-F-F)F-F-,
*F&F(F'F-F+F-F(F-F-#F*\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
46 "alias(d= RootOf(2*x^2+x-e*x+2)); factor(hh,d);" }}{PARA 8 "" 1 "" 
{TEXT -1 48 "Error, (in RootOf) expression independent of, _Z" }}
{PARA 8 "" 1 "" {TEXT -1 99 "Error, (in factor) 2nd argument is not a \+
valid algebraic extension, RootOf(2*_Z^2+(1-5^(1/2))*_Z+2)" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "roots(f,e);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#7#7$\"\"!\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 33 "readlib(split); hhh:=split(h,x); " }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#:6%%\"aG%\"xG%\"sG6$%\"fG%\"LG6#%fnCopyright~(c)~1995~W
aterloo~Maple~Inc.~All~rights~reserved.G6\"C%>8$--%(readlibG6#%'splits
G6%9$9%.8%@$/9#\"\"$>9&F:*&--%\"@G6$%&evalaG%'NormalG6#&F06#\"\"\"FK-%
(convertG6$-%$mapG6$:6#F&F-F-F-)&F7FJ&F76#\"\"#F-F-&F0FW%\"*GFKF-F-" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$hhhG**,,%\"xG\"\"\"F(F(-%'RootOfG6
#,,*$%#_ZG\"\"%F(*$F.\"\"$F(*$F.\"\"#F(F.F(F(F(F(*$F)F3F(*$F)F1F(F(,&F
'F(F)!\"\"F(,&F'F(F4F7F(,&F'F(F5F7F(" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 13 "alias(aa=%1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&%\"I
G%\"dG%\"eG%#aaG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "hhh;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#**,,%\"xG\"\"\"F&F&%#aaGF&*$F'\"\"#F&*
$F'\"\"$F&F&,&F%F&F'!\"\"F&,&F%F&F(F-F&,&F%F&F*F-F&" }}}{EXCHG {PARA 
256 "" 0 "" {TEXT -1 1 " " }{TEXT 256 23 "On traite l'exercice 1." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "t:=24165438790;" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>%\"tG\",!zQa;C" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 203 "isprime(t);#attention c'est un test probabiliste : s
i elle retourne false le nombre est assur\351ment compos\351; si elle \+
retourne true  il y a de fortes chances que t soit premier mais ce n'e
st pas s\373r !!!!!!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%&falseG" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "ifactor(t);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#**-%!G6#\"\"#\"\"\"-F%6#\"\"&F(-F%6#\"%z7F(-F%6#\"
(,%*)=F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "nextprime(t);# \+
retourne le plus petit nombre premier strictement suprieur  t" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#\",$zQa;C" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 13 "prevprime(t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"
,j(Qa;C" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "n:= 10; for j fr
om 1 to n do ithprime( j) od;#29 est le dixi\350me nombre premier" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"nG\"#5" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"$" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#\"\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#6" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"#8" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#<" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#\"#>" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#B
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#H" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 61 "AUTOUR des NOMBRES PREMIERS\nque fait la fonction ci-dess
ous ?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "pi1:=x->nops(selec
t(isprime,[$1..x]));pi1(30);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$pi1
G:6#%\"xG6\"6$%)operatorG%&arrowGF(-%%nopsG6#-%'selectG6$%(isprimeG7#-
%\"$G6#;\"\"\"9$F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#5" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "myli:=x->int(1/ln(t), t=2..x
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{MPLTEXT 1 0 93 "plot(\{pi1,myli\},0..10);plot(\{pi1,myli\},100..1000,
title=`Comportement asymptotique de pi(x)`);" }}{PARA 13 "" 1 "" 
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\\]w/$\"++/)4X)F3F\\]w/$\"+q)**3.*F3F\\]w/$\"+%4DCa*F3F\\]wFg\\w/Fj\\w
%$20.GF]]wF`]w/Fd]w%$50.GFf]wFi]wF\\^wF_^wFb^w/Fg^w%%200.GFi^wF\\_w/F`
_w%%500.GFb_wFe_wFh_wF[`w" 2 341 341 341 2 0 1 0 2 9 0 4 1 1.000000 
45.000000 45.000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 
0 0 0 0 0 }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 96 "iquo(t,27);irem
(t,27);# calcule le quotient et le reste de la division (euclidienne) \+
de t par 27" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"*^i,&*)" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#\"#8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
25 "igcd(458,26);ilcm(56,15);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$S)" }}}{EXCHG {PARA 257 "" 0 "
" {TEXT -1 51 "On peut m\352me lui faire faire l'algorithme d'Euclide
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "u:='u'; v:='v'; d:=igcd
ex(458,13, u,v); u;v; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"uGF$" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"vGF$" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"dG\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!\"%" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#\"$T\"" }}}{EXCHG {PARA 258 "" 0 "" {TEXT 
-1 105 "igcdex(a,b,u,v) calcule le pgcd de a et de b et met dans u et \+
v les entiers relatifs  tels que au +bv =1." }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 18 "igcdex(35,12,u,v);" }}{PARA 8 "" 1 "" {TEXT -1 52 
"Error, (in igcdex) Illegal use of a formal parameter" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "u;v;# les variables u et v doivent \+
\352tre non affect\351es !!!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!\"%" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$T\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 9 "t mod 27;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#8" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 111 "1/3 mod 27; # 3 n'est pas i
nversible dans Z/27 Z; bravo pour la notation qui vous vaudrait .....u
n z\351ro point\351!" }}{PARA 8 "" 1 "" {TEXT -1 41 "Error, the modula
r inverse does not exist" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 
"1/3 mod  37;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#D" }}}{EXCHG 
{PARA 259 "" 0 "" {TEXT -1 10 "Question 2" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 145 "restart; Sol:= msolve(x^4 = 1 , 33);# 33 correspon
d  Z/33Z msolve (r\351soud modulo) n\351cessite deux arguments par ex \+
: msolve(equation, congruence) " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$
SolG6&<#/%\"xG\"#B<#/F(\"\"\"<#/F(\"#5<#/F(\"#K" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 91 "sol :=msolve(x^2 = -1 , 33) ;solu:=msolve(x^2 \+
= -4 , 33) ;# quand il n'y a pas de solutions" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$solG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%soluG6
\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 102 "solut:= msolve(x^585
 = x ,45); solut:= msolve(x^11= x , 11);# on v\351rifie le petit th
\351or\350me de Fermat !" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%&solutG6
1<#/%\"xG\"#5<#/F(\"#F<#/F(\"\")<#/F(\"#G<#/F(\"\"*<#/F(\"\"!<#/F(\"#E
<#/F(\"#N<#/F(\"#O<#/F(\"#W<#/F(\"\"\"<#/F(\"#=<#/F(\"#P<#/F(\"#><#/F(
\"#<" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&solutG<#/%\"xGF'" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "msolve(\{3*x+4*y=5,2*x+5*y=1
\},11);#on peut faire des syst\350mes" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#<$/%\"xG\"\"$/%\"yG\"#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
40 "result :=isolve (5767*x + 15987*y =146);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%'resultG<$/%\"xG,&!#(*\"\"\"%$_N1G!$>#/%\"yG,&\"#NF*F
+\"#z" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "u:='u'; v:='v'; d:
=igcdex(5767,15987, u,v); u;v; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%
\"uGF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"vGF$" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%\"dG\"#t" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#h" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#!#A" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 55 "5767*122-44*15987;#il n'y a pas unicit\351 (bien s
\373r )...." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$Y\"" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "subs(_N1=10, result);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#<$/%\"xG!%(G#/%\"yG\"$D)" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 55 "solve(-97-219*_N1=61,_N1);resultat:=subs(_N1=
\",result);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##!$e\"\"$>#" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%)resultatG<$/%\"xG\"#h/%\"yG#!%<[\"$>#" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "nops(resultat);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 25 "simplify(op(2,resultat));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/
%\"yG#!%<[\"$>#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "4817/219;
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6##\"%<[\"$>#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "whatty
pe(\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%)fractionG" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "irem(4817,219);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#\"$=#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "i
quo(4817,219);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#@" }}}{EXCHG 
{PARA 262 "" 0 "" {TEXT -1 140 "Chercher l'analogue des fonctions PGCD
,PPCM pour les polyn\364mes..... Il y a d'ailleurs bien d'autres comma
ndes int\351ressantes dans le package " }{TEXT 257 11 "numtheory, " }
{TEXT -1 71 "en particulier tout ce qui concerne les racines primitive
s de l'unit\351 :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "restar
t:with(numtheory);phi(27);phi(7);" }}{PARA 7 "" 1 "" {TEXT -1 33 "Warn
ing, new definition for order" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7fn%
\"BG%\"FG%&GIgcdG%\"JG%\"LG%\"MG%*bernoulliG%)bigomegaG%&cfracG%)cfrac
polG%+cyclotomicG%)divisorsG%&eulerG%)factorEQG%*factorsetG%'fermatG%(
ifactorG%)ifactorsG%)imagunitG%&indexG%)invcfracG%'invphiG%'isolveG%(i
sprimeG%*issqrfreeG%)ithprimeG%'jacobiG%*kroneckerG%'lambdaG%)legendre
G%)mcombineG%)mersenneG%*minkowskiG%(mipolysG%%mlogG%'mobiusG%&mrootG%
&msqrtG%)nearestpG%*nextprimeG%*nthconverG%)nthdenomG%)nthnumerG%'nthp
owG%&orderG%)pdexpandG%$phiG%*pprimrootG%*prevprimeG%)primrootG%(quadr
esG%+rootsunityG%*safeprimeG%&sigmaG%*sq2factorG%(sum2sqrG%$tauG%%thue
G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#=" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "?fe
rmat;# calcule les nombres  de la forme 2^(2^n)+1" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 16 "fermat(6,'w');w;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"5<;b4P2WnW=" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%;it~i
s~completely~factored~G*&-%!G6#,&**-F&6#\"\"#\"\")-F&6#\"\"$F,-F&6#\"
\"(\"\"\"-F&6#\"#<F4F4F4F4F4-F&6#,&*,F*F--F&6#\"\"&F4-F&6#\"#ZF4-F&6#
\"$t$F4-F&6#\"(z#)*HF4F4F4F4F4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 48 "F(9448,'w');w;#c'est fait de fa\347on intelligente!" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#%/object~too~bigG" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6$%:it~has~this~prime~factor~G,&*&-%!G6#\"\"#\"%]%*-F'6#
\"#>\"\"\"F.F.F." }}}{EXCHG {PARA 263 "" 0 "" {TEXT -1 389 "L'arithm
\351tique sert entre autres \340 faire le cryptage de vos messages Int
ernet (cf cours alg\350bre second semestre) . L'algorithme de base (cr
yptographie \340 cl\351 publique) date de 1978 s'appelle RSA du nom de
s inventeurs (Rivest, Shamir et Adelman). Comme quoi il ne faut jurer \+
de rien de nos jours, m\352me des notions de maths que d'aucun trouve \+
tr\350s abstraites peuvent avoir des applications ! " }}}}{MARK "73 0 \+
0" 293 }{VIEWOPTS 1 1 0 1 1 1803 }