A051085 - OEIS

%I #19 Sep 08 2022 08:44:59

%S 2,3,11,19,43,59,67,83,107,131,139,163,179,211,227,251,281,283,307,

%T 331,347,379,419,443,467,491,499,523,547,563,571,587,617,619,643,659,

%U 683,691,739,787,811,827,859,883,907,947,971,1019,1033,1049,1051,1091,1097,1123,1163,1171

%N Primes p such that x^32 = -2 has a solution mod p.

%C Complement of A216747 relative to A000040. - _Vincenzo Librandi_, Sep 17 2012

%H Vincenzo Librandi, <a href="/A051085/b051085.txt">Table of n, a(n) for n = 1..1000</a>

%t ok[p_]:= Reduce[Mod[x^32 + 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[400]], ok] (* _Vincenzo Librandi_, Sep 15 2012 *)

%o (PARI)

%o forprime(p=2, 2000, if([]~!=polrootsmod(x^32+2, p), print1(p, ", "))); print();

%o /* _Joerg Arndt_, Jun 24 2012 */

%o (Magma) [p: p in PrimesUpTo(1200) | exists(t){x : x in ResidueClassRing(p) | x^32 eq - 2}]; // _Vincenzo Librandi_, Sep 15 2012

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_

%E More terms from _Joerg Arndt_, Jul 27 2011