A051081 Primes p such that x^24 = -2 has a solution mod p.

2, 3, 11, 43, 59, 83, 107, 131, 179, 227, 251, 257, 281, 283, 307, 347, 419, 443, 467, 491, 499, 563, 587, 617, 643, 659, 683, 691, 739, 811, 827, 881, 947, 971, 1019, 1049, 1051, 1091, 1097, 1163, 1187, 1193, 1217, 1259, 1283, 1307, 1427, 1451, 1459, 1481

Offset

1,1

Comments

Complement of A216743 relative to A000040. - Vincenzo Librandi, Sep 17 2012

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Maple

isA051081 := proc(p) local x; for x from 0 to p-1 do if (x^24 mod p) = (-2 mod p) then RETURN(true) ; fi; od: RETURN(false) ; end: for i from 1 to 300 do p := ithprime(i) ; if isA051081(p) then printf("%d, ", p) ; fi; od: # R. J. Mathar, Oct 15 2008

Mathematica

ok[p_]:= Reduce[Mod[x^24 + 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[500]], ok] (* Vincenzo Librandi, Sep 15 2012 *)

Prog

(PARI) /* see A051071 */
(Magma) [p: p in PrimesUpTo(1500) | exists(t){x : x in ResidueClassRing(p) | x^24 eq - 2}]; // Vincenzo Librandi, Sep 15 2012

Crossrefs

Sequence in context: A055692 A051075 A051087 * A051093 A107327 A162101

Adjacent sequences: A051078 A051079 A051080 * A051082 A051083 A051084

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from R. J. Mathar, Oct 15 2008

Status

approved