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Numbers n such that n | 12^n + 11^n + 10^n + 9^n.
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%I #4 Mar 30 2012 17:30:26

%S 1,2,3,7,9,21,27,49,57,63,81,119,147,171,189,243,343,399,441,446,513,

%T 567,729,1029,1083,1197,1323,1539,1701,2187,2401,2793,2943,2979,3087,

%U 3249,3591,3969,4617,5103,5831,6561,7047,7203,7581,7791,8001,8379,8829

%N Numbers n such that n | 12^n + 11^n + 10^n + 9^n.

%t Select[ Range[ 1, 10^5 ], Mod[ PowerMod[ 12, #, # ] + PowerMod[ 11, #, # ] + PowerMod[ 10, #, # ] + PowerMod[ 9, #, # ], # ] == 0 & ]

%K nonn

%O 1,2

%A _Robert G. Wilson v_, Sep 20 2000