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Primes p such that x^56 = -2 has a solution mod p.
2

%I #20 Sep 08 2022 08:44:59

%S 2,3,11,19,59,67,83,107,131,139,163,179,227,251,257,283,307,331,347,

%T 419,443,467,499,523,563,571,587,619,643,683,691,739,787,811,859,881,

%U 907,947,971,1019,1033,1049,1091,1097,1123,1163,1171,1187,1193,1217,1249,1259,1283,1291,1307,1427,1451,1459,1481,1483,1523,1531,1553,1571,1579

%N Primes p such that x^56 = -2 has a solution mod p.

%C Complement of A216773 relative to A000040. - _Vincenzo Librandi_, Sep 17 2012

%H Vincenzo Librandi, <a href="/A051097/b051097.txt">Table of n, a(n) for n = 1..1000</a>

%t ok[p_]:= Reduce[Mod[x^56 + 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[500]], ok] (* _Vincenzo Librandi_, Sep 16 2012 *)

%o (PARI) forprime(p=2,2000,if([]~!=polrootsff(x^56+2,p,y-1),print1(p,", ")));print();

%o /* or: */

%o forprime(p=2,2000,if([]~!=polrootsmod(x^56+2,p),print1(p,", ")));print(); /* faster */

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

%o (Magma) [p: p in PrimesUpTo(1600) | exists(t){x : x in ResidueClassRing(p) | x^56 eq - 2}]; // _Vincenzo Librandi_, Sep 16 2012

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_

%E More terms from _Joerg Arndt_, Jul 27 2011