DS d`informatique Nombres premiers, nombres composés

n > 1 1 n
a b (a, b)
N, a ∈ZN(a, N)=1
aN−1= 1 (mod N)
a, q, N aqmod N
a, N
N
J(M, N)∈ {−1,0,1}
M, N N > 1
k∈ZJ(M+kN, N) = J(M, N)
a, b ∈ZJ(ab, N) = J(a, N) J(b, N)
J(0, N) = 0
J(1, N) = 1
J(−1, N)=(−1)N−1
2
J(2, N) = (−1)N2−1
8

M > 1 J(M, N) = (−1)(M−1)(N−1)
4J(N, M)
N, a ∈ZN
a
N−1
2= J(a, N) (mod N)
13280 = 1 (mod 561) a= 13
N= 561
M, N N
J(M, N)
a, N
N
N
N
N
√N
B
B
2B
2
X
p≤X
1
p=O(log log X)
X