INFORMATIQUE - Concours Centrale

Concours Centrale - Supélec 2007
Épreuve : INFORMATIQUE Filière MP
fn
f0= 0 f1= 1 n∈N
fn+2 =fn+fn+1
fn
fn
n
fnf
fn
n
fn
fkk6n
fn
n
Xn=fn
fn+1A=0 1 1 1Xn+1 =AXn
n∈NXn=AnX0
fn
fnk
n>1An=fn−1fn
fnfn+1
f2nf2n+1 f2n+2 fn
fn+1
Q ϕ :Q→Z/2Z
n
n O(n)
un=O(vn)vn=O(un)un= Θ(vn)
un=O(vn)
nΘ(n2)
O(n2)
a[b]a b
a b
n
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- version du 30 avril 2007 20h1

INFORMATIQUE Filière MP
pαi6n < pαi+1 P9= 23.32.5.7
Pkk∈[[1, n]]
h
(pα, p)p
Pk(pα, p)p
k α k < pα
P9(16,2) (27,3)
(25,5) (49,7)
(a, b)<1(a0, b0)
a<a0
62
(4,2) Pk−1
Pk
•k k
(k2, k)
•(pα, p)k=pαp
(pα+1, p)
Pkk
3k= 16
h n h = Θ(ln n)
Pnn
q ϕ(q) = fn[2]
f2050 [2]
f0f0
n=fn[2] 3
n n
m>3g g0= 0
g1=g2=· · · =gm−1= 1 gn+m=gn+gn+m−1
n∈Ngn+mgngn+m−1
m n gn
g
m= 3
n gn
m n
gnO(n)
g
gnOmax(n, m)m
g1020 m= 1000
n∈N6n
Pn=pα1
1· · · pαk
kp1, p2, ..., pk
2n i αi
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INFORMATIQUE Filière MP
ln Pn∼n n
Pn
••• •••
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