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A051098 Primes p such that x^58 = -2 has a solution mod p.

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%I A051098 #17 Sep 08 2022 08:44:59
%S A051098 2,3,11,17,19,41,43,67,73,83,89,97,107,113,131,137,139,163,179,193,
%T A051098 211,227,241,251,257,281,283,307,313,331,337,347,353,379,401,409,419,
%U A051098 433,443,449,457,467,491,499,521,547,563,569,571,577,587,593,601,617,619,641,643,659,673,683,691,739,761,769,787,809,811,827,857,859,881,883,907,937,947,953,971,977,1009
%N A051098 Primes p such that x^58 = -2 has a solution mod p.
%C A051098 Complement of A216774 relative to A000040. - _Vincenzo Librandi_, Sep 17 2012
%H A051098 Vincenzo Librandi, <a href="/A051098/b051098.txt">Table of n, a(n) for n = 1..1000</a>
%t A051098 ok[p_]:= Reduce[Mod[x^58 + 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[500]], ok] (* _Vincenzo Librandi_, Sep 16 2012 *)
%o A051098 (PARI) /* see A051071 */
%o A051098 (Magma) [p: p in PrimesUpTo(1010) | exists(t){x : x in ResidueClassRing(p) | x^58 eq - 2}]; // _Vincenzo Librandi_, Sep 16 2012
%K A051098 nonn,easy
%O A051098 1,1
%A A051098 _N. J. A. Sloane_
%E A051098 More terms from _Joerg Arndt_, Jul 27 2011