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A051073 Primes p such that x^8 = -2 has a solution mod p.

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%I A051073 #24 May 08 2025 08:55:56
%S A051073 2,3,11,19,43,59,67,83,107,131,139,163,179,211,227,251,257,281,283,
%T A051073 307,331,337,347,379,419,443,467,491,499,523,547,563,571,587,617,619,
%U A051073 643,659,683,691,739,787,811,827,859,881,883,907,947,971,1019
%N A051073 Primes p such that x^8 = -2 has a solution mod p.
%C A051073 Complement of A216735 relative to A000040. - _Vincenzo Librandi_, Sep 16 2012
%H A051073 Vincenzo Librandi, <a href="/A051073/b051073.txt">Table of n, a(n) for n = 1..1000</a>
%t A051073 ok[p_]:= Reduce[Mod[x^8 + 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[500]], ok] (* _Vincenzo Librandi_, Sep 15 2012 *)
%o A051073 (PARI)
%o A051073 forprime(p=2, 2000, if([]~!=polrootsmod(x^8+2, p), print1(p, ", "))); print();
%o A051073 /* _Joerg Arndt_, Jun 24 2012 */
%o A051073 (Magma) [p: p in PrimesUpTo(1200) | exists(t){x : x in ResidueClassRing(p) | x^8 eq - 2}]; // _Vincenzo Librandi_, Sep 15 2012
%Y A051073 Cf. A000040, A216735.
%K A051073 nonn,easy
%O A051073 1,1
%A A051073 _N. J. A. Sloane_
%E A051073 More terms from _Joerg Arndt_, Jun 24 2012