A045318 - OEIS

%I #20 Jun 26 2022 23:24:53

%S 5,7,17,19,29,31,37,41,43,53,61,67,73,79,89,97,101,103,113,127,137,

%T 139,149,151,157,163,173,193,197,199,211,223,233,241,257,269,271,281,

%U 283,293,307,317,331,337,349,353,367,373,379,389,397

%N Primes p such that x^8 = 3 has no solution mod p.

%C Complement of A045317 relative to A000040. - _Vincenzo Librandi_, Sep 19 2012

%H Vincenzo Librandi, <a href="/A045318/b045318.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 19 2012 *)

%o (Magma) [p: p in PrimesUpTo(500) | not exists{x : x in ResidueClassRing(p) | x^8 eq 3} ]; // _Vincenzo Librandi_, Sep 19 2012

%Y Cf. A000040, A045317, A301916, A320481.

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_