Problème "petites Mines" 1

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a P ∈R[X]
un+1 =aun+P(n)P
Ea,b =u∈RN/∃b∈R/∀n∈N, un+1 =aun+b
Ea,b
x1y= (an)n∈N
{x, y}
Ea,b
a6= 1
a6= 1 m∈N
Ea,m =u∈RN/∃P∈Rm[X]/∀n∈N, un+1 =aun+P(n)
ϕ:Rm[X]→Rm+1 ϕ(P) = (P(0), ..., P (m))
u∈Ea,m P∈Rm[X]∀n∈N, un+1 =
aun+P(n)Pu
Ea,m
θ:Ea,m →R[X]θ(u) = Puθ
(θ)
k∈NQk= (X+ 1)k−aXk
Qk
{Q0, Q1, ..., Qm}Rm[X]
k∈J0, mKQk∈(θ) (θ)
Ea,m
k∈J0, mKxk= (nk)n∈Ny= (an)n∈N
{x0, ..., xm, y}Ea,m
u0=−2∀n∈N, un+1 = 2un−2n+ 7
a= 1
P∈R[X]un+1 =un+P(n)
u0=−2∀n∈N, un+1 =un−6n+ 1
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