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Numbers n such that n | 12^n + 11^n + 10^n + 9^n + 8^n + 7^n + 6^n + 5^n + 4^n.
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%I #6 Jul 15 2014 11:15:41

%S 1,2,3,4,6,9,12,21,27,63,81,106,147,189,243,372,441,567,729,861,1029,

%T 1323,1701,2187,2241,3087,3594,3969,4347,4473,5103,5622,5966,6561,

%U 7203,9261,11907,12231,12663,15309,19683,20204,21609,27783,32628,32907

%N Numbers n such that n | 12^n + 11^n + 10^n + 9^n + 8^n + 7^n + 6^n + 5^n + 4^n.

%t Select[ Range[ 10^5 ], Mod[ PowerMod[ 12, #, # ] + PowerMod[ 11, #, # ] + PowerMod[ 10, #, # ] + PowerMod[ 9, #, # ] + PowerMod[ 8, #, # ] + PowerMod[ 7, #, # ] + PowerMod[ 6, #, # ] + PowerMod[ 5, #, # ] + PowerMod[ 4, #, # ], # ] == 0 & ]

%t Select[Range[33000],Divisible[Total[Range[4,12]^#],#]&] (* _Harvey P. Dale_, Jul 15 2014 *)

%K nonn

%O 1,2

%A _Robert G. Wilson v_, Sep 22 2000