Exercice 1 [Un calcul simple] Exercice 2 [Décomposition d`un

a b
y←− 0
b6= 0
b
y←− y+a
b←− bb/2c
b6= 0
a←− 2a
y
b
a p
A a A[X]
n p A[X]m k
n < km a
a=a0+a1p+· · · +ak−1pk−1
i∈ {0, . . . , k−1}aiA[X]
m
a0
aim
ai
a p r q a0
q
ai(km)2−km2
A
A[X]n
m A[X] 2m(n−m+ 1) A

m1, . . . , mrr>1r > 1
a1, . . . , arr
(S) : x≡aimod mi(1 6i6r)
M=Q16i6rmi
x=
r
X
i=1
ai(M−1
imod mi)Mi,
Mi=Y
j6=i
mj.
(S)r= 3 m1= 7 m2= 11 m3= 13 a1= 3
a2= 6 a3= 7
miai
x(S) [0, M[
i= 2 r
Ci←− 1
j= 1 i−1
u←− m−1
jmod mi
Ci←− u·Cimod mi
u←− a1x←− u
i= 2 r
u←− (ai−x)·Cimod mi
x←− x+u·Qi−1
j=1 mj
x
r= 3 m1= 7 m2= 11 m3= 13 a1= 3 a2= 6
a3= 7
y∈[0, M[y=
b1+b2m1+b3m1m2+· · · +bnm1· · · mn−1bi∈[0, mi[
bix miai
(S)
[0, M[