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%I #16 Sep 08 2022 08:44:53
%S 11,31,61,71,101,131,151,181,191,211,241,251,271,281,311,331,401,421,
%T 461,521,541,571,601,631,641,691,701,751,811,821,881,911,941,971,991,
%U 1031,1061,1151,1181,1201,1231,1291,1301,1321,1361,1381,1451,1481,1531
%N Primes p such that x^5 = 3 has no solution mod p.
%C Complement of A040161 relative to A000040. - _Vincenzo Librandi_, Sep 18 2012
%H Vincenzo Librandi, <a href="/A040162/b040162.txt">Table of n, a(n) for n = 1..1000</a>
%t ok[p_]:= Reduce[Mod[x^5 - 3, p] == 0, x, Integers] == False; Select[Prime[Range[300]], ok] (* _Vincenzo Librandi_, Sep 18 2012 *)
%o (Magma) [ p: p in PrimesUpTo(1600) | forall(t){x : x in ResidueClassRing(p) | x^5 ne 3} ]; // _Klaus Brockhaus_, Jun 03 2009
%o (Magma) [p: p in PrimesUpTo(1550) | not exists{x : x in ResidueClassRing(p) | x^5 eq 3} ]; // _Vincenzo Librandi_, Sep 18 2012
%Y Cf. A040161 (primes p such that x^5 = 3 has a solution mod p).
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_
%E More terms from _Klaus Brockhaus_, Jun 03 2009
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