计

计

иㄠ┪穦倒拜筁硂妓拜肈 620000 琌ぐ或硂讽礛ぃ螟и笵 6 よ经 (Power)  626364 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 ㎝ 6ㄤ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ㄢА 0 n = 0璝ㄢА 1   n = 1

璝иだㄢ家い 1 0ê獽眔琌 5 ┪ 6 计

パ计 (Automorphic Prime) 度5

顶计

ир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 24875 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ㄢА 0 n = 0璝ㄢА 1   n = 1硂㎝计筽璝ㄢА - 1 ê獽琌иǎ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 , 13 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.