计
计
иㄠ┪穦倒拜筁硂妓拜肈 620000 琌ぐ或硂讽礛ぃ螟и笵 6 よ经 (Power) 626364 单琌 6パ崩阶 620000 琌 6
ㄤ龟硂ㄇ竒筁程ソ计ご玂ㄓ计计и嘿计 (Automorphic Number)
ㄇ计ㄒ
计 | 赣计キよ |
1 | 1 |
5 | 25 |
6 | 36 |
25 | 625 |
76 | 5776 |
376 | 141376 |
625 | 390625 |
9376 | 87909376 |
(OEIS A003226) | |
иぃ螟祇瞷埃 1 ㄤ緇计琌 5 ㎝ 6ㄤ龟硂ぃ螟瞶秆
安砞Τ琘 k 计 n
n2 = a * 10k + n
n2 - n = a * 10k
n2 - n = 0 (mod 10k)
n (n - 1) = 0 (mod 2k) の n (n - 1) = 0 (mod 5k)
琌珿 n だ家 2k の 5k い单 0 ┪ 1璝ㄢА 0 n = 0璝ㄢА 1 n = 1
璝иだㄢ家い 1 0ê獽眔琌 5 ┪ 6 计
パ计 (Automorphic Prime) 度5
顶计
ир计いキよ阀├崩約ミよ计竒筁ミよ程ソ计ご玂ㄓ计计и嘿顶计 (Trimorphic Number)
ㄇ顶计ㄒ
顶计 | 赣计ミよ |
1 | 1 |
4 | 64 |
5 | 125 |
6 | 216 |
9 | 729 |
24 | 13824 |
25 | 15625 |
49 | 117649 |
51 | 132651 |
75 | 421875 |
76 | 438976 |
99 | 970299 |
125 | 1953125 |
249 | 15438249 |
251 | 15813251 |
375 | 52734375 |
376 | 53157376 |
499 | 124251499 |
501 | 125751501 |
624 | 242970624 |
625 | 244140625 |
749 | 420189749 |
751 | 423564751 |
875 | 669921875 |
999 | 997002999 |
(OEIS A033819) | |
и笵计穦妓琌顶计はㄓ弧玥ぃ﹚ 9 24875 单ぃ琌计
иョт 9 99 999 单ㄇ计 (Repdigit)τ睲︹琌 9 ㎡拜琌┮Τ硂摸计琌顶计㎡氮琌﹚
安砞Τ琘 k 顶计 n
n3 = a * 10k + n
n3 - n = a * 10k
n3 - n = 0 (mod 10k)
n (n - 1) (n + 1) = 0 (mod 2k) の n (n - 1) (n + 1) = 0 (mod 5k)
琌珿 n だ家 2k の 5k い单 0 1 ┪ -1璝ㄢА 0 n = 0璝ㄢА 1 n = 1硂㎝计筽璝ㄢА - 1 ê獽琌иǎ计
痙種翴硂柑家 2k 笲衡龟籔キ盽笲衡ぃ┮眔秆┪穦家 8 埃 -1, 0 , 13 ョ琌秆家 32 15 琌秆单
籔秈闽计贺
ㄤ龟иョ秈﹚竡计┪蔼顶计ê 1 讽礛ヴ秈ㄤ龟ヴ籔计┪计闽计贺计攀计 (Narcissistic Number)獂计 (Pandigital Number) ┪じ计 (Repunit) 单﹚竡ぃ秈い糤╯癸禜
把σゅ膍の呼
Wikipedia. "Automorphic Number" From Wikipedia. http://en.wikipedia.org/wiki/Automorphic_number.
Wikipedia. "Trimorphic Number" From Wikipedia. http://en.wikipedia.org/wiki/Trimorphic_number.