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%I #7 Feb 12 2022 18:25:57
%S 1,3,5,9,15,25,27,45,75,81,125,135,225,243,345,375,405,625,675,729,
%T 1025,1125,1215,1863,1875,2025,2187,2375,2875,3125,3375,3645,4395,
%U 5625,5875,6075,6561,8145,9225,9375,10125,10935,14015,14523,15525,15625
%N Numbers n such that n | 12^n + 11^n + 10^n + 9^n + 8^n + 7^n + 6^n + 5^n + 4^n + 3^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, #, # ] + PowerMod[ 3, #, # ], # ] == 0 & ]
%t Select[Range[16000],Divisible[Total[Range[3,12]^#],#]&] (* _Harvey P. Dale_, Dec 06 2013 *)
%t Select[Range[16000],Mod[Total[PowerMod[Range[3,12],#,#]],#]==0&] (* _Harvey P. Dale_, Feb 12 2022 *)
%K nonn
%O 1,2
%A _Robert G. Wilson v_, Sep 22 2000
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