1 Entiers rationnels

Z
ϕ

Q
Z/Zn

R=Z/Zn k n k
x≡a m
x≡b n m
n x mn

a= 1105 b= 208 d a b x, y ∈Z
d=ax +by
L p Mp= 2p−1
p∈L Pp= 2p−1Mp
n≥0
pn= 2 + n[1
1 +
n+1
P
k=2
[(n+ 2)/k −[(n+ 1)/k]]
]
[]
L pn0≤n≤100
P L
r P P r
a
q
a q
N N
a q
Fnn[0,1]
≤nF1= [0,1] FnFn−1
a
b
c
d
a+c
b+db+d≤n
FnF10

x≡6 17
x≡5 11
x≡3 9
3x≡10 17
p= 7 n= 6
(Z/pnZ)∗
1 + p(Z/pnZ)∗
multiplicative order()
(Z/pnZ)∗
n
0l−1
0ABCDEF GHIJKLMNOP QRST UV W XY Zabcdefghijklmnopqrstuvwxyz., ; : 0
l= 57
n= 43657458478029293976669622635814729303016339791
p q
c= 3
C:Z/Zn−→ Z/Zn
x−→ xc
L l −1
L N l
N n M
n−1