A040106 - OEIS

%I #9 Sep 08 2022 08:44:53

%S 3,7,13,17,23,29,37,41,43,47,53,61,67,73,83,89,97,103,107,113,127,137,

%T 157,163,167,173,193,197,223,227,229,233,241,257,263,277,281,283,293,

%U 307,313,317,337,347,349,353,367

%N Primes p such that x^4 = 5 has no solution mod p.

%C Complement of A040105 relative to A000040. - _Vincenzo Librandi_, Sep 17 2012

%H Vincenzo Librandi, <a href="/A040106/b040106.txt">Table of n, a(n) for n = 1..1000</a>

%t ok[p_]:= Reduce[Mod[x^4 - 5, p] == 0, x, Integers] == False;Select[Prime[Range[100]], ok] (* _Vincenzo Librandi_, Sep 17 2012  *)

%o (Magma) [p: p in PrimesUpTo(500) | not exists{x : x in ResidueClassRing(p) | x^4 eq 5} ]; // _Vincenzo Librandi_, Sep 17 2012

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_.