世界上最大的互异完全n次数

今天，闲来无聊，解决了一个困扰十年的问题。

大概在上高一的时候。一直想着有个问题：
有这样一个完全平方书，它的每个数位上的数字都不相同。我把它成为： 互异完全2次数
那他最大是多大呢？
那最大的 完全立方数是多少呢？还有4次方呢？


答案：9814072356    32461759   5764801  


Current Power Number: 2
Match Data: 9814072356
Match Data: 9761835204
Match Data: 9614783025
Match Data: 9560732841
Match Data: 9351276804
Match Data: 9054283716
Match Data: 8967143025
Match Data: 8503421796
Match Data: 8391476025
Match Data: 8326197504
Match Data: 8135679204
Match Data: 8127563409
Match Data: 8125940736
Match Data: 8014367529
Match Data: 7984316025
Match Data: 7946831025
Match Data: 7935068241
Match Data: 7854036129
Match Data: 7680594321
Match Data: 7408561329
Match Data: 7362154809
Match Data: 7351862049
Match Data: 7285134609
Match Data: 7165283904
Match Data: 7042398561
Match Data: 6714983025
Match Data: 6597013284
Match Data: 6471398025
Match Data: 6457890321
Match Data: 6154873209
Match Data: 6095237184
Match Data: 5982403716
Match Data: 5803697124
Match Data: 5783146209
Match Data: 5739426081
Match Data: 5273809641
Match Data: 5102673489
Match Data: 4832057169
Match Data: 4730825961
Match Data: 4728350169
Match Data: 4580176329
Match Data: 4392508176
Match Data: 4369871025
Match Data: 4308215769
Match Data: 4307821956
Match Data: 3985270641
Match Data: 3975428601
Match Data: 3964087521
Match Data: 3928657041
Match Data: 3827401956
Match Data: 3791480625
Match Data: 3719048256
Match Data: 3528716409
Match Data: 3428570916
Match Data: 3416987025
Match Data: 3412078569
Match Data: 3285697041
Match Data: 3195867024
Match Data: 3094251876
Match Data: 3089247561
Match Data: 3082914576
Match Data: 3074258916
Match Data: 3015986724
Match Data: 2913408576
Match Data: 2571098436
There are 65 in total.

Current Power Number: 3
Match Data: 32461759
Match Data: 27543608
Match Data: 26198073
Match Data: 24137569
Match Data: 8365427
Match Data: 3048625
Match Data: 2460375
Match Data: 912673
Match Data: 804357
Match Data: 681472
Match Data: 592704
Match Data: 438976
Match Data: 421875
Match Data: 389017
Match Data: 328509
Match Data: 287496
Match Data: 205379
Match Data: 68921
Match Data: 54872
Match Data: 42875
Match Data: 32768
Match Data: 24389
Match Data: 19683
Match Data: 13824
Match Data: 10648
Match Data: 9261
There are 26 in total.

Current Power Number: 4
Match Data: 5764801
Match Data: 5308416
Match Data: 3748096
Match Data: 2085136
Match Data: 1048576
Match Data: 390625
Match Data: 279841
Match Data: 104976
Match Data: 83521
Match Data: 38416
Match Data: 28561
Match Data: 20736
Match Data: 4096
Match Data: 2401
Match Data: 1296
Match Data: 625
Match Data: 256
Match Data: 81
Match Data: 16
There are 19 in total.

Current Power Number: 5
Match Data: 79235168
Match Data: 1048576
Match Data: 537824
Match Data: 32768
Match Data: 16807
Match Data: 3125
Match Data: 1024
Match Data: 243
Match Data: 32
There are 9 in total.

Current Power Number: 6
Match Data: 24137569
Match Data: 4096
Match Data: 729
Match Data: 64
There are 4 in total.

Current Power Number: 7
Match Data: 78125
Match Data: 16384
Match Data: 2187
Match Data: 128
There are 4 in total.

Current Power Number: 8
Match Data: 5764801
Match Data: 390625
Match Data: 256
There are 3 in total.

Current Power Number: 9
Match Data: 19683
Match Data: 512
There are 2 in total.

Current Power Number: 10
Match Data: 1048576
Match Data: 1024
There are 2 in total.

Current Power Number: 11
Match Data: 2048
There are 1 in total.

Current Power Number: 12
Match Data: 4096
There are 1 in total.

Current Power Number: 13
Match Data: 8192
There are 1 in total.

Current Power Number: 14
Match Data: 16384
There are 1 in total.

Current Power Number: 15
Match Data: 32768
There are 1 in total.