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%I #22 Aug 20 2023 16:56:50
%S 1,2,3,4,6,12
%N Numbers k such that j^j == j^j^j (mod k) for every j.
%C Divisors of 12. For k <= 16, we may compute membership directly (see Mathematica code). For k > 16, we have j = 2 as a counterexample. - _Eric M. Schmidt_, Aug 03 2014
%t h1[mod_] := Table[PowerMod[i, i, mod], {i, 1, mod + LCM[mod*CarmichaelLambda[mod]]}]; h2[mod_] := Table[PowerMod[i, i^i, mod], {i, 1, mod + LCM[mod*CarmichaelLambda[mod]]}]; Union[Table[If[h1[i] == h2[i], Print[i]; i], {i, 1000}]]
%K nonn,fini,full
%O 1,2
%A _José María Grau Ribas_, Jan 23 2012