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N & n (Posted on 2014-01-27) Difficulty: 2 of 5
N is a m-th power of an integer.
It consists of n distinct digits, averaging n.

Find n,m and N, using your head + pen and paper only.

Check, whether there exist additional solutions (computer allowed).

Clearly, n>1; m>1 - to exclude trivial cases.

No Solution Yet Submitted by Ady TZIDON    
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98 results not requiring "distinct" Comment 7 of 7 |

 144       =   12 ^ 2
 216       =   6 ^ 3
 225       =   15 ^ 2
 243       =   3 ^ 5
 324       =   18 ^ 2
 441       =   21 ^ 2
 900       =   30 ^ 2
 1681      =   41 ^ 2
 3364      =   58 ^ 2
 3481      =   59 ^ 2
 4624      =   68 ^ 2
 7225      =   85 ^ 2
 9025      =   95 ^ 2
 12769     =   113 ^ 2
 14884     =   122 ^ 2
 24649     =   157 ^ 2
 24964     =   158 ^ 2
 27556     =   166 ^ 2
 30976     =   176 ^ 2
 33856     =   184 ^ 2
 37249     =   193 ^ 2
 37636     =   194 ^ 2
 44944     =   212 ^ 2
 48841     =   221 ^ 2
 56644     =   238 ^ 2
 65536     =   256 ^ 2
 65536     =   16 ^ 4
 65536     =   4 ^ 8
 65536     =   2 ^ 16
 66049     =   257 ^ 2
 70756     =   266 ^ 2
 75076     =   274 ^ 2
 75625     =   275 ^ 2
 80089     =   283 ^ 2
 80656     =   284 ^ 2
 85264     =   292 ^ 2
 96721     =   311 ^ 2
 149769    =   387 ^ 2
 173889    =   417 ^ 2
 178929    =   423 ^ 2
 199809    =   447 ^ 2
 278784    =   528 ^ 2
 279936    =   6 ^ 7
 287496    =   66 ^ 3
 288369    =   537 ^ 2
 294849    =   543 ^ 2
 389376    =   624 ^ 2
 439569    =   663 ^ 2
 459684    =   678 ^ 2
 467856    =   684 ^ 2
 471969    =   687 ^ 2
 509796    =   714 ^ 2
 589824    =   768 ^ 2
 599076    =   774 ^ 2
 617796    =   786 ^ 2
 660969    =   813 ^ 2
 665856    =   816 ^ 2
 675684    =   822 ^ 2
 685584    =   828 ^ 2
 695556    =   834 ^ 2
 746496    =   864 ^ 2
 751689    =   867 ^ 2
 759375    =   15 ^ 5
 767376    =   876 ^ 2
 777924    =   882 ^ 2
 788544    =   888 ^ 2
 793881    =   891 ^ 2
 799236    =   894 ^ 2
 853776    =   924 ^ 2
 859329    =   927 ^ 2
 870489    =   933 ^ 2
 876096    =   936 ^ 2
 884736    =   96 ^ 3
 887364    =   942 ^ 2
 898704    =   948 ^ 2
 915849    =   957 ^ 2
 927369    =   963 ^ 2
 938961    =   969 ^ 2
 944784    =   972 ^ 2
 956484    =   978 ^ 2
 968256    =   984 ^ 2
 970299    =   99 ^ 3
 974169    =   987 ^ 2
 986049    =   993 ^ 2
 2778889   =   1667 ^ 2
 4695889   =   2167 ^ 2
 5678689   =   2383 ^ 2
 5697769   =   2387 ^ 2
 5938969   =   2437 ^ 2
 6568969   =   2563 ^ 2
 6589489   =   2567 ^ 2
 6848689   =   2617 ^ 2
 6895876   =   2626 ^ 2
 7974976   =   2824 ^ 2
 7997584   =   2828 ^ 2
 8779369   =   2963 ^ 2
 9878449   =   3143 ^ 2
 9966649   =   3157 ^ 2

Indeed there are no 8-digit results and of course no 9-digit.


  Posted by Charlie on 2014-01-27 15:48:49
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