%I #13 Jun 26 2022 23:24:39

%S 2,3,11,13,23,47,59,71,83,107,109,131,167,179,181,191,227,229,239,251,

%T 263,277,311,313,347,359,383,419,421,431,433,443,467,479,491,503,541,

%U 563,587,599,601,647,659,683,709

%N Primes p such that x^8 = 3 has a solution mod p.

%C Complement of A045318 relative to A000040. - _Vincenzo Librandi_, Sep 13 2012

%H Vincenzo Librandi, <a href="/A045317/b045317.txt">Table of n, a(n) for n = 1..1000</a>

%t ok[p_]:= Reduce[Mod[x^8- 3, p] == 0, x, Integers]=!=False; Select[Prime[Range[200]], ok] (* _Vincenzo Librandi_, Sep 13 2012 *)

%o (Magma) [p: p in PrimesUpTo(800) | exists(t){x : x in ResidueClassRing(p) | x^8 eq 3}]; // _Vincenzo Librandi_, Sep 13 2012

%o (PARI) isok(p) = isprime(p) && ispower(Mod(3, p), 8); \\ _Michel Marcus_, Oct 17 2018

%Y Cf. A000040, A045318.

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_