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%I #14 Jun 09 2023 08:00:34
%S 3,5,11,13,19,29,37,43,53,59,61,67,71,83,101,107,109,113,127,131,139,
%T 149,157,163,173,179,181,197,211,227,229,239,251,269,277,281,283,293,
%U 307,317,331,337,347,349,373,379,389,397,419,421,443,449,461,463,467
%N Primes p such that x^14 = 2 has no solution mod p.
%C Complement of A049546 relative to A000040.
%H Vincenzo Librandi, <a href="/A059265/b059265.txt">Table of n, a(n) for n = 1..1000</a>
%t Select[ Prime@Range[2, 93], FreeQ[ Mod[x^14 /. x -> Range[ # ], # ], 2] &] (* _Robert G. Wilson v_, Dec 15 2005 *)
%t ok[p_] := Reduce[Mod[x^14 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[100]], ok] (* _Vincenzo Librandi_, Sep 20 2012 *)
%o (Magma) [p: p in PrimesUpTo(500) | not exists{x: x in ResidueClassRing(p) | x^14 eq 2} ]; // _Vincenzo Librandi_, Sep 20 2012
%Y Cf. A000040, A049546.
%K nonn,easy
%O 1,1
%A _Klaus Brockhaus_, Jan 23 2001
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