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Numbers n such that n | 5^n + 4^n + 3^n + 2^n.
1

%I #8 Mar 01 2023 14:43:58

%S 1,2,6,7,49,78,91,133,343,539,1014,1309,1578,2401,3367,4459,10231,

%T 12103,12246,12691,13182,16807,45619,97193,117649,120883,149989,

%U 159198,171366,199283,218491,347263,675703,823543,1100687,1294139,1327753,1336699,1486807

%N Numbers n such that n | 5^n + 4^n + 3^n + 2^n.

%p A057249:=n->`if`(type((5^n+4^n+3^n+2^n)/n, integer), n, NULL); seq(A057249(n), n=1..10^6); # _Wesley Ivan Hurt_, Mar 09 2014

%t Select[ Range[ 10^6 ], Mod[ PowerMod[ 5, #, # ] + PowerMod[ 4, #, # ] + PowerMod[ 3, #, # ] + PowerMod[ 2, #, # ], # ] == 0 & ]

%t Select[Range[15*10^5],Mod[Total[PowerMod[Range[2,5],#,#]],#]==0&] (* _Harvey P. Dale_, Mar 01 2023 *)

%K nonn

%O 1,2

%A _Robert G. Wilson v_, Sep 21 2000

%E a(35)-a(39) from _Wesley Ivan Hurt_, Mar 09 2014