1 / 9
涔?/p>
棰?/p>
鍥?/p>
4.1.
鑻ョ兢
G
鐨勫厓绱?/p>
a
鍧囧彲琛ㄧず涓烘煇涓�鍏冪礌
x
鐨勫箓锛屽嵆
a
=
x
m
锛屽垯绉拌繖涓兢涓哄惊鐜兢銆傝嫢缇ょ殑
鍏冪礌浜ゆ崲寰嬫垚绔嬶紝鍗?/p>
a
,
b
飪?/p>
G
婊¤冻
a
飪?/p>
b
=
b
飪?/p>
a
鍒欑О杩欎釜缇や负闃胯礉灏?/p>
(Abel)
缇わ紝璇曡瘉鏄庢墍鏈夌殑寰幆缇ら兘鏄樋璐濆皵缇ゃ�?/p>
[
璇?/p>
].
璁惧惊鐜兢
(
G
,
飪?/p>
)
鐨勭敓鎴愬厓鏄?/p>
x
0
飪?/p>
G
銆?/p>
浜庢槸锛?/p>
瀵逛换浣曞厓绱?/p>
a
,
b
飪?/p>
G
锛?/p>
飥?/p>
m
锛?/p>
n
飪?/p>
N
锛?/p>
浣垮緱
a
=
x
0
m
,
b
=
x
0
n
,
浠庤�?/p>
a
飪?/p>
b
=
x
0
m
飪?/p>
x
0
n
=
x
0
m
+
n
(
鎸囨暟寰?/p>
)
=
x
0
n
+
m
(
鏁扮殑鍔犳硶浜ゆ崲寰?/p>
)
=
x
0
n
飪?/p>
x
0
m
(
鎸囨暟寰?/p>
)
=
b
飪?/p>
a
鏁?/p>
飪?/p>
杩愮畻婊¤冻浜ゆ崲寰嬶紱鍗?/p>
(
G
,
飪?/p>
)
鏄氦鎹㈢兢銆?/p>
4.2.
鑻?/p>
x
鏄兢
G
鐨勪竴涓厓绱狅紝瀛樺湪涓�涓渶灏忕殑姝ｆ暣鏁?/p>
m
锛?/p>
浣?/p>
x
m
=
e
锛屽垯绉?/p>
m
涓?/p>
x
鐨勯樁锛?/p>
璇曡瘉锛?/p>
C
={
e
,
x
,
x
2
,
飩?/p>
,
x
m
-1
}
鏄?/p>
G
鐨勪竴涓瓙缇ゃ�?/p>
[
璇?/p>
].(1)
闈炵┖鎬?/p>
C
飩癸儐
锛氬洜涓?/p>
飥?/p>
e
飪?/p>
G
锛?/p>
(2)
鍖呭惈鎬?/p>
C
飪?/p>
G
锛氬洜涓?/p>
x
飪?/p>
G
锛屾牴鎹兢
G
鐨勫皝闂�э紝鍙煡
x
2
,
飩?/p>
,
x
m
-1
,
(
x
m
=)
e
飪?/p>
G
锛屾晠
C
飪?/p>
G
锛?/p>
(3)
灏侀棴鎬?/p>
飥?/p>
a
,
b
飪?/p>
C
飪?/p>
a
飪?/p>
b
飪?/p>
C
锛?/p>
飥?/p>
a
,
b
飪?/p>
C
锛?/p>
飥?/p>
k
锛?/p>
l
飪?/p>
N
(0
飩?/p>
k
<
m
锛?/p>
0
飩?/p>
l
<
m
)
锛?/p>
浣?/p>
a
=
x
k
,
b
=
x
l
锛?/p>
浠庤�?/p>
a
飪?/p>
b
=
x
k
飪?/p>
x
l
=
x
(
k
+
l
) mod
m
飪?/p>
C
(
鍥犱负
0
飩?/p>
(
k
+
l
) mod
m
<
m
)
锛?/p>
(4)
鏈夐�嗗厓
飥?/p>
a
飪?/p>
C
飪?/p>
a
-1
飪?/p>
C
锛?/p>
飥?/p>
a
飪?/p>
C
锛?/p>
飥?/p>
k
飪?/p>
N
(0
飩?/p>
k
<
m
)
锛屼娇
a
=
x
k
,
浠庤�?/p>
a
-1
=
x
m
-k
飪?/p>
C
(
鍥犱负
0
飩?/p>
m
-
k
<
m
)
銆?/p>
缁煎悎
(1) (2) (3) (4)
锛屽彲鐭?/p>
(
C
,
飪?/p>
)
鏄?/p>
(
G
,
飪?/p>
)
鐨勪竴涓瓙缇ゃ�?/p>
4.3.
鑻?/p>
G
鏄樁涓?/p>
n
鐨勬湁闄愮兢锛屽垯
G
鐨勬墍鏈夊厓绱犵殑闃堕兘涓嶈秴杩?/p>
n
銆?/p>
[
璇?/p>
].
瀵逛换涓�鍏冪礌
x
飪?/p>
G
锛岃鍏堕樁涓?/p>
m
锛屽苟浠?/p>
C
={
e
,
x
,
x
2
,
飩?/p>
,
x
m
-1
}
锛屽垯鐢变範棰?/p>
4.2.
鍙煡
(
C
,
飪?/p>
)
鏄?/p>
(
G
,
飪?/p>
)
鐨勪竴涓瓙缇わ紝鏁呭叿鏈夊寘鍚�?/p>
C
飪?/p>
G
銆傚洜姝ゆ湁
m
= |
C
|
飩?/p>
|
G
| =
n
鎵�浠ョ兢
G
鐨勬墍鏈夊厓绱犵殑闃堕兘涓嶈秴杩?/p>
n
銆?/p>
4.4.
鑻?/p>
G
鏄樁涓?/p>
n
鐨勫惊鐜兢锛屾眰缇?/p>
G
鐨勬瘝鍏冪礌鐨勬暟鐩紝鍗?/p>
G
鐨勫厓绱犲彲浠ヨ〃绀烘垚
a
鐨勫箓锛?/p>
a
,
a
2
,
飩?/p>
,
a
n
鐨勫厓绱?/p>
a
鐨勬暟鐩�?/p>
[
璇?/p>
].
璁?/p>
(
G
,
飪?/p>
)
鏄惊鐜兢锛?/p>
a
鏄叾涓�涓瘝鍏冪礌
(
鐢熸垚鍏?/p>
)
锛?/p>
a
鐨勯樁涓?/p>
n
(
涔熸槸
G
鐨勯樁
)
锛屽垯
G
={
a
,
a
2
,
飩?/p>
,
a
n
(=
e
) }
銆?/p>
(1).
鎴戜滑鏉ヨ瘉锛氬浠讳綍鑷劧鏁?/p>
r
飪?/p>
N
(0<
r
<
n
锛?/p>
(
r
,
n
) = 1)
锛屽厓绱?/p>
a
r
飪?/p>
G
閮芥槸
G
鐨勪竴涓瘝鍏冪礌
(
鐢熸垚鍏?/p>
)
銆?/p>
涓烘锛屽彧闇�璇?/p>
a
r
鐨勯樁涓?/p>
n
鍗冲彲銆?/p>
棣栧厛锛?/p>
璁?/p>
a
r
鐨勯樁涓?/p>
k
锛?/p>
鍥犳鏈?/p>
a
r
飪?/p>
k
= (
a
r
)
k
=
e
锛?/p>
鐢变簬
a
鐨勯樁涓?/p>
n
锛?/p>
鏁呮牴鎹紩鐞?/p>
*
鍙緱
n
|
r
飪?/p>
k
銆?/p>
宸茬煡
0<
r
<
n
锛?/p>
(
r
,
n
) = 1
锛屽洜姝ゅ彧鑳芥湁
n
|
k
锛屾墍浠?/p>
n
飩?/p>
k
銆?/p>
鍏舵锛?/p>
(
a
r
)
n
=
a
r
飪?/p>
n
(
鎸囨暟寰?/p>
)
=
a
n
飪?/p>
r
(
鏁扮殑鍔犳硶浜ゆ崲寰?/p>
)
=(
a
n
)
r
(
鎸囨暟寰?/p>
)
=
e
r
=
e
銆?/p>
鍥犺�岋紝鐢?/p>
k
鏄厓绱?/p>
a
r
鐨勯樁锛屽叿鏈夋渶灏忔�э紝鎵�浠?/p>
k
飩?/p>
n
銆?/p>