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{SECT 0 {EXCHG {PARA 261 "" 0 "" {TEXT -1 42 "TP3 S\311QUENCES, LISTES
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0 72 "seq([`  cos(pi/`||n||`)`,cos(Pi/n),convert(cos(Pi/n),radical)],n
=1..17);" }}{PARA 12 "" 1 "" {XPPMATH 20 "637%%,~~cos(pi/1)G!\"\"F%7%%
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0 "" 0 "" {TEXT -1 280 "Maple est flemmard : en effet, pour n =  16 et
 17 il y a des expressions avec radicaux, mais il ne les calcule pas, \+
m\352m en utisant convert(.., radical) ; par contre, pour n =7,9,11,13
,14,  il est d\351montr\351 qu'il n'existe en effet pas d'expression a
vec radicaux (th\351or\350me de Gauss)." }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 1 "2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "A:=\{seq(s
eq(a^2+b^2,a=0..10),b=0..10)\} intersect \{seq(k,k=1..100)\};nops(A);
\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"AG<M\"\"\"\"\"#\"\"%\"\"&\"
\")\"\"*\"#5\"#8\"#;\"#<\"#=\"#?\"#D\"#E\"#H\"#K\"#M\"#O\"#P\"#S\"#T\"
#X\"#\\\"#]\"#_\"#`\"#e\"#h\"#k\"#l\"#o\"#s\"#t\"#u\"#!)\"#\")\"##)\"#
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}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "B:=select(is,A,odd);map(x
->x-1,B);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG<5\"\"\"\"\"&\"\"*
\"#8\"#<\"#D\"#H\"#P\"#T\"#X\"#\\\"#`\"#h\"#l\"#t\"#\")\"#&)\"#*)\"#(*
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0 "" 0 "" {TEXT -1 291 "On donc peut penser qu'une somme de deux carr
\351s qui est impaire est forc\351ment de la forme 4k + 1 ; ceci est e
xact car si une somme de deux carr\351s est impaire, l'un est pair et \+
l'autre impair, et un carr\351 pair est toujours multiple de 4, tandis
 qu'un carr\351 impair est un multiple de 4 plus 1." }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "A:=\{seq
(seq(seq(seq(a^2+b^2+c^2+d^2,a=0..10),b=0..10),c=0..10),d=0..10)\} int
ersect \{seq(k,k=1..100)\};nops(A);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6
#>%\"AG<`q\"\"\"\"\"#\"\"$\"\"%\"\"&\"\"'\"\"(\"\")\"\"*\"#5\"#6\"#7\"
#8\"#9\"#:\"#;\"#<\"#=\"#>\"#?\"#@\"#A\"#B\"#C\"#D\"#E\"#F\"#G\"#H\"#I
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}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 105 "On donc peut penser que tout n
aturel est somme de 4 carr\351s, ce qui est exact, mais difficile \340
 d\351montrer." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "A:=\{seq(
seq(seq(a^2+b^2+c^2,a=0..10),b=0..10),c=0..10)\}intersect \{seq(k,k=1.
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=A)\}:C:=(B intersect \{seq(k,k=1..100)\})minus A;" }}{PARA 12 "" 1 "
" {XPPMATH 20 "6#>%\"AG<ap\"\"\"\"\"#\"\"$\"\"%\"\"&\"\"'\"\")\"\"*\"#
5\"#6\"#7\"#8\"#9\"#;\"#<\"#=\"#>\"#?\"#@\"#A\"#C\"#D\"#E\"#F\"#H\"#I
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{EXCHG {PARA 0 "" 0 "" {TEXT -1 113 "C est l'ensemble des nombres entr
e 0 et 100 qui sont produit de 2 sommes de 3 carr\351s sans \352tre so
mme de 3 carr\351s." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 1 "3" }}}
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