login
Numbers n such that n | 11^n + 10^n + 9^n + 8^n + 7^n + 6^n + 5^n + 4^n + 3^n.
1

%I #7 Jun 09 2021 13:17:37

%S 1,3,7,9,21,27,49,63,69,81,119,147,189,243,343,441,567,729,1029,1269,

%T 1323,1701,2187,2401,3087,3357,3969,5103,5271,5831,6561,7203,9261,

%U 9639,11907,15309,16767,16807,19683,20727,21609,24451,27783,30429,35077

%N Numbers n such that 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[ 11, #, # ] + PowerMod[ 10, #, # ] + PowerMod[ 9, #, # ] + PowerMod[ 8, #, # ] + PowerMod[ 7, #, # ] + PowerMod[ 6, #, # ] + PowerMod[ 5, #, # ] + PowerMod[ 4, #, # ] + PowerMod[ 3, #, # ], # ] == 0 & ]

%t Select[Range[36000],Mod[Total[Table[PowerMod[n,#,#],{n,3,11}]],#] == 0&] (* This program is essentially equivalent to the above program. *) (* _Harvey P. Dale_, Jun 09 2021 *)

%K nonn

%O 1,2

%A _Robert G. Wilson v_, Sep 22 2000