A040125 - OEIS

%I #18 Sep 08 2022 08:44:53

%S 5,7,13,17,19,29,31,41,43,53,67,73,79,89,97,101,103,109,113,127,137,

%T 139,149,151,163,173,181,197,199,211,223,229,233,241,257,269,271,277,

%U 281,283,293,307,317,331,337,353

%N Primes p such that x^4 = 12 has no solution mod p.

%C Complement of A040124 relative to A000040. - _Vincenzo Librandi_, Sep 17 2012

%H Vincenzo Librandi, <a href="/A040125/b040125.txt">Table of n, a(n) for n = 1..1000</a>

%t Select[Prime[Range[PrimePi[400]]], ! MemberQ[PowerMod[Range[#], 4, #], Mod[12, #]] &] (* _T. D. Noe_, Sep 13 2012 *)

%t ok[p_]:= Reduce[Mod[x^4 - 12, p] == 0, x, Integers] == False;Select[Prime[Range[100]], ok] (* _Vincenzo Librandi_, Sep 17 2012  *)

%o (Magma) [p: p in PrimesUpTo(400) | forall{x: x in ResidueClassRing(p) | x^4 ne 12}]; // _Bruno Berselli_, Sep 12 2012

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_.