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1p
0 1 .1q 0 1 =1p+q 0 1 ,
H
H
1 1
0 1 .
H
0 1
1 0 −1
.1 1
0 1 .0 1 1 0 =1 0 1 1 6∈ H .
A B Z1SL(2,Z)
A3=−I A6=I A 6
B2=−I B 4
BA =1 1
0 1 H H ⊂< A, B >
A B H
BA A B
H
AB 6=BA
A I, A, A2, A3=
−I, A4=−A, A5=−A2B
I, B, −I, −B A, A2,−A, −A2
B, −B
G G Z Z/nZ
n > 0G kZk
Z/mZm
n G
{a1,· · · , an} ⊂ Qai=pi/qii∈ {1,· · · , n}q qi
aiQ1/q H
ai<1/q >
HQ
Q
Q Q

255 = 3 ×5×17 G255 n17
G n 1 17 255
17k+ 1 n= 1
G17 G
A0=Z/4Z×Z/4ZA0
A1={(a, a)∈Z/4Z×Z/4Z|a∈Z/4Z},
A2={(a, b)∈Z/4Z×Z/4Z|b−a∈ {0,2}} .
(1,1)
A⊂Z/4Z×Z/4ZA(0,0) (1,1)
A A1
A(a, a+1) (a, a)∈
A1(a+ 1, a + 1) A(0,1) (−1,0)
A(1,0) (0,1) A=A0A
(a, a −1)
A(a, a + 2) A
A1A2⊂A
A=A2A=A1
B=F×F0B{0} × F0F× {0}
I⊂B{0}B I
(a, b)a6= 0 b6= 0 a b I
(a, b).(a−1, b−1) = (1,1) I=B a b
a I (a0,0) a06= 0
I(a0, b) (1,1) I(0, b0)
I b0∈F0I
(0, b).(0, b0.b−1) = (0, b0)I={0} × F0
b I =F× {0}
B
A a, b, c ∈A\{0}
d= (a, b)d|a d|b cd|ca cd|cb cd|(ca, cb)
u, v ∈A d =au +bv cd =cau +cbv
(ca, cb)|cd cd = (ca, cb)
x∈A x|( (a, b), c)x|(a, b)x|c x|a x|b x|c
x|(a, (b, c))
A
(a, b)∼1 (a, c)∼1a b
c bc (a, bc)∼1
(a, b)∼1a b a|bc
a bc
c a|c

(b, c) = 1 b c b|a
b a
c bc a
bc|a
n∈N∗a6=−1,0,1p
p|a p2a
Xn−aQ
X4−8X3+ 12X2−6X+ 2 p= 2
X5−12X3+ 36X−12 p= 3 p= 4 4