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Primes p such that x^4 = -2 has a solution mod p.
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%I #18 Sep 08 2022 08:44:59

%S 2,3,11,19,43,59,67,73,83,89,107,113,131,139,163,179,211,227,233,251,

%T 257,281,283,307,331,337,347,353,379,419,443,467,491,499,523,547,563,

%U 571,577,587,593,601,617,619,643,659,683,691,739,787,811,827,859,881,883,907,937,947,971,1019,1033,1049,1051,1091,1097,1123

%N Primes p such that x^4 = -2 has a solution mod p.

%C Complement of A216690 relative to A000040. - _Vincenzo Librandi_, Sep 16 2012

%H Vincenzo Librandi, <a href="/A051071/b051071.txt">Table of n, a(n) for n = 1..1000</a>

%t ok[p_]:= Reduce[Mod[x^4 + 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[200]], ok] (* _Vincenzo Librandi_, Sep 15 2012 *)

%o (PARI)

%o forprime(p=2,2000,if([]~!=polrootsff(x^4+2,p,y-1),print1(p,", ")));print();

%o /* or: */

%o forprime(p=2,2000,if([]~!=polrootsmod(x^4+2,p),print1(p,", ")));print();

%o /* faster */ /* _Joerg Arndt_, Jul 27 2011 */

%o (Magma) [p: p in PrimesUpTo(1200) | exists(t){x : x in ResidueClassRing(p) | x^4 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