Théorème de Dirichlet (version faible)

n m
m+λn λ
n≥1 1 + λn λ
n≥1p a
p an−1
d n d 6=n p ad−1
Φm, m ∈N∗,
Xn−1 = Qd|nΦddeg Φn=ϕ(n)
Φn∈Z[X]
m6=nΦmΦnQ[X]
B(X) = Qd|n,d6=nΦd
ΦnBQ[X]
U, V ∈Z[X]a
a=U(X)Φn(X) + V(X)B(X).
aΦn(a)6= 0 Φn(a)6=±1
pΦn(a)p a

n≥1p n
(ZpZ)∗
n≥1p1+λn λ ∈N∗
n
Φn(X) = Y
ζ
(X−ζ)
ζ n C
Φn(X)n= 1,2,3,4,6,8
Φp(X)p
Xn−1 = Qd|nΦddeg Φn=ϕ(n)
Φn∈Z[X]
n
m6=nΦmΦnQ[X]
pΦp(X)Q[X]Z[X]
nΦnZ[X]Q[X]
Φn0 1 −1