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%I #18 Sep 08 2022 08:44:59
%S 2,3,11,43,59,83,107,131,179,227,251,257,281,283,307,347,419,443,467,
%T 491,499,563,587,617,643,659,683,691,739,811,827,947,971,1019,1049,
%U 1051,1091,1097,1163,1187,1193,1259,1283,1307,1427,1451,1459,1481,1499,1523
%N Primes p such that x^48 = -2 has a solution mod p.
%C Complement of A216769 relative to A000040. - _Vincenzo Librandi_, Sep 17 2012
%H Vincenzo Librandi, <a href="/A051093/b051093.txt">Table of n, a(n) for n = 1..1000</a>
%p isA051093 := proc(p) local x; for x from 0 to p-1 do if (x^48 mod p) = (-2 mod p) then RETURN(true) ; fi; od: RETURN(false) ; end: for i from 1 to 300 do p := ithprime(i) ; if isA051093(p) then printf("%d,",p) ; fi; od: # _R. J. Mathar_, Oct 15 2008
%t ok[p_]:= Reduce[Mod[x^48 + 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[500]], ok] (* _Vincenzo Librandi_, Sep 16 2012 *)
%o (PARI) /* see A051071 */
%o (Magma) [p: p in PrimesUpTo(1550) | exists(t){x : x in ResidueClassRing(p) | x^48 eq - 2}]; // _Vincenzo Librandi_, Sep 16 2012
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_
%E Extended by _R. J. Mathar_, Oct 15 2008
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