淇℃伅瀹夊叏鏁板鍩虹涔犻绛旀
绗竴绔?/p>
鏁存暟鐨勫彲闄ゆ�?/p>
1
锛庤瘉鏄庯細鍥犱负
2|n
鎵�浠?/p>
n=2k ,
k
飪?/p>
Z
5|n
鎵�浠?/p>
5|2k
锛?/p>
鍙堬紙
5
锛?/p>
2
锛?/p>
=1
锛屾墍浠?/p>
5|k
鍗?/p>
k=5
k
1
锛?/p>
k
1
飪?/p>
Z
7|n
鎵�浠?/p>
7|2*5
k
1
,
鍙堬紙
7
锛?/p>
10
锛?/p>
=1
锛屾墍浠?/p>
7|
k
1
鍗?/p>
k
1
=7
k
2
锛?/p>
k
2
飪?/p>
Z
鎵�浠?/p>
n=2*5*7
k
2
鍗?/p>
n=70 k
2
,
k
2
飪?/p>
Z
鍥犳
70|n
2
锛庤瘉鏄庯細鍥犱负
a
3
-a=(a-1)a(a+1)
褰?/p>
a=3k
锛?/p>
k
飪?/p>
Z 3|a
鍒?/p>
3|a
3
-a
褰?/p>
a=3k-1
锛?/p>
k
飪?/p>
Z 3|a+1
鍒?/p>
3|a
3
-a
褰?/p>
a=3k+1
锛?/p>
k
飪?/p>
Z 3|a-1
鍒?/p>
3|a
3
-a
鎵�浠?/p>
a
3
-a
鑳借
3
鏁撮櫎銆?/p>
3
锛庤瘉鏄庯細浠绘剰濂囨暣鏁板彲琛ㄧず涓?/p>
2
k
0
+1
锛?/p>
k
0
飪?/p>
Z
锛?/p>
2
k
0
+1
锛?/p>
2
锛?/p>
4
k
0
2
+4
k
0
+1=4
k
0
(
k
0
+1)+1
鐢变簬
k
0
涓?/p>
k
0
+1
涓轰袱杩炵画鏁存暟锛屽繀鏈変竴涓负鍋舵暟锛屾墍浠?/p>
k
0
(
k
0
+1)=2k
鎵�浠ワ紙
2
k
0
+1
锛?/p>
2
=8k+1
寰楄瘉銆?/p>
4
锛庤瘉鏄庯細璁句笁涓繛缁暣鏁颁负
a-1,a,a+1
鍒?/p>
(a-1)a(a+1)= a
3
-a
鐢辩浜岄缁撹
3|
锛?/p>
a
3
-a
锛?/p>
鍗?/p>
3|(a-1)a(a+1)
鍙堜笁涓繛缁暣鏁颁腑蹇呮湁鑷冲皯涓�涓负鍋舵暟锛屽垯
2|(a-1)a(a+1)
鍙堬紙
3
锛?/p>
2
锛?/p>
=1
鎵�浠?/p>
6|(a-1)a(a+1)
寰楄瘉銆?/p>
5
锛庤瘉鏄庯細鏋勯�犱笅鍒?/p>
k
涓繛缁鏁存暟鍒楋細
(k+1)
锛?/p>
+2, (k+1)
锛?/p>
+3, (k+1)
锛?/p>
+4,
鈥︹�?/p>
, (k+1)
锛?/p>
+(k+1), k
飪?/p>
Z
瀵规暟鍒椾腑浠讳竴鏁?/p>
(k+1)
锛?/p>
+i=i[(k+1)k
鈥?/p>
(i+1)(i-1)
鈥?/p>
2*1+1], i=2,3,4,
鈥?/p>
(k+1)
鎵�浠?/p>
i|(k+1)
锛?/p>
+i
鍗?/p>
(k+1)
锛?/p>
+i
涓哄悎鏁?/p>
鎵�浠ユ
k
涓繛缁鏁存暟閮芥槸鍚堟暟銆?/p>
6
锛庤瘉鏄庯細鍥犱负
191
1/2
锛?/p>
14 ,
灏忎簬
14
鐨勭礌鏁版湁
2
锛?/p>
3
锛?/p>
5
锛?/p>
7
锛?/p>
11
锛?/p>
13
缁忛獙绠楅兘涓嶈兘鏁撮櫎
191
鎵�浠?/p>
191
涓虹礌鏁般�?/p>
鍥犱负
547
1/2
锛?/p>
24 ,
灏忎簬
24
鐨勭礌鏁版湁
2
锛?/p>
3
锛?/p>
5
锛?/p>
7
锛?/p>
11
锛?/p>
13
锛?/p>
17
锛?/p>
19
锛?/p>
23
缁忛獙绠楅兘涓嶈兘鏁撮櫎
547
鎵�浠?/p>
547
涓虹礌鏁般�?/p>
鐢?/p>
737=11*67 ,747=3*249
鐭?/p>
737
涓?/p>
747
閮戒负鍚堟暟銆?/p>
8
锛庤В锛氬瓨鍦ㄣ�?/p>
eg
锛?/p>
a=6,b=2,c=9
10
锛庤瘉鏄庯細
p
1
p
2
p
3
|n
锛?/p>
鍒?/p>
n= p
1
p
2
p
3
k
锛?/p>
k
飪?/p>
N
+
鍙?/p>
p
1
鈮?/p>
p
2
鈮?/p>
p
3
锛屾墍浠?/p>
n= p
1
p
2
p
3
k
鈮?/p>
p
1
3
鍗?/p>
p
1
3
鈮?/p>
n
1/3
p
1
涓虹礌鏁?/p>
鍒?/p>
p
1
鈮?/p>
2
锛屽張
p
1
鈮?/p>
p
2
鈮?/p>
p
3
锛屾墍浠?/p>
n= p
1
p
2
p
3
k
鈮?/p>
2
p
2
p
3
鈮?/p>
2
p
2
2
鍗?/p>
p
2
鈮?/p>
(
n/2)
1/2
寰楄瘉銆?/p>
11
锛庤В锛氬皬浜庣瓑浜?/p>
500
1/2
鐨勬墍鏈夌礌鏁颁负
2
锛?/p>
3
锛?/p>
5
锛?/p>
7
锛?/p>
11
锛?/p>
13
锛?/p>
17
锛?/p>
19
锛屼緷娆″垹闄よ繖浜涚礌鏁扮殑
鍊嶆暟鍙緱鎵�姹傜礌鏁帮細
12
锛庤瘉鏄庯細鍙嶈瘉娉?/p>
鍋囪
3k+1
娌℃湁鐩稿悓褰㈠紡鐨勭礌鍥犳暟锛?/p>
鍒欏畠涓�瀹氬彧鑳借〃绀烘垚鑻ュ共褰㈠
3k-1
鐨勭礌鏁扮浉
涔樸�?/p>
(3
k
1
+1)(3
k
2
+1)=[( 3
k
1
+1)
k
2
+
k
1
]*3+1
鏄剧劧鑻ュ共涓?/p>
3k+1
鐨勭礌鏁扮浉涔橈紝寰?