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A051085 Primes p such that x^32 = -2 has a solution mod p.

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%I A051085 #21 May 30 2025 15:45:42
%S A051085 2,3,11,19,43,59,67,83,107,131,139,163,179,211,227,251,281,283,307,
%T A051085 331,347,379,419,443,467,491,499,523,547,563,571,587,617,619,643,659,
%U A051085 683,691,739,787,811,827,859,883,907,947,971,1019,1033,1049,1051,1091,1097,1123,1163,1171
%N A051085 Primes p such that x^32 = -2 has a solution mod p.
%C A051085 Complement of A216747 relative to A000040. - _Vincenzo Librandi_, Sep 17 2012
%H A051085 Vincenzo Librandi, <a href="/A051085/b051085.txt">Table of n, a(n) for n = 1..1000</a>
%t A051085 ok[p_]:= Reduce[Mod[x^32 + 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[400]], ok] (* _Vincenzo Librandi_, Sep 15 2012 *)
%o A051085 (PARI)
%o A051085 forprime(p=2, 2000, if([]~!=polrootsmod(x^32+2, p), print1(p, ", "))); print();
%o A051085 /* _Joerg Arndt_, Jun 24 2012 */
%o A051085 (Magma) [p: p in PrimesUpTo(1200) | exists(t){x : x in ResidueClassRing(p) | x^32 eq - 2}]; // _Vincenzo Librandi_, Sep 15 2012
%Y A051085 Cf. A163183.
%K A051085 nonn,easy
%O A051085 1,1
%A A051085 _N. J. A. Sloane_
%E A051085 More terms from _Joerg Arndt_, Jul 27 2011