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%I #18 Sep 08 2022 08:44:53
%S 11,31,41,61,71,101,131,181,191,211,271,281,311,331,401,421,461,491,
%T 521,541,601,631,661,691,701,751,761,811,821,881,941,991,1021,1031,
%U 1051,1061,1091,1151,1171,1201,1231,1291,1301,1321,1361,1381,1451,1471,1481,1511,1531,1571
%N Primes p such that x^5 = 2 has no solution mod p.
%C Complement of A040159 relative to A000040. - _Vincenzo Librandi_, Sep 18 2012
%H Vincenzo Librandi, <a href="/A040160/b040160.txt">Table of n, a(n) for n = 1..1000</a>
%t ok[p_]:= Reduce[Mod[x^5 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[300]], ok] (* _Vincenzo Librandi_, Sep 18 2012 *)
%o (Magma) [p: p in PrimesUpTo(1300) | forall{x: x in ResidueClassRing(p) | x^5 ne 2}]; // _Bruno Berselli_, Sep 12 2012
%o (Magma) [p: p in PrimesUpTo(1500) | not exists{x : x in ResidueClassRing(p) | x^5 eq 2} ]; // _Vincenzo Librandi_, Sep 18 2012
%o (PARI) forprime(p=2,10^3,if(#polrootsmod(x^5-2,p)==0,print1(p,", "))) \\ _Joerg Arndt_, Jul 16 2015
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_.
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