A051093 Primes p such that x^48 = -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, 947, 971, 1019, 1049, 1051, 1091, 1097, 1163, 1187, 1193, 1259, 1283, 1307, 1427, 1451, 1459, 1481, 1499, 1523

Offset

1,1

Comments

Complement of A216769 relative to A000040. - Vincenzo Librandi, Sep 17 2012

Links

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

Maple

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

Mathematica

ok[p_]:= Reduce[Mod[x^48 + 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[500]], ok] (* Vincenzo Librandi, Sep 16 2012 *)

Prog

(PARI) /* see A051071 */
(Magma) [p: p in PrimesUpTo(1550) | exists(t){x : x in ResidueClassRing(p) | x^48 eq - 2}]; // Vincenzo Librandi, Sep 16 2012

Crossrefs

Sequence in context: A051075 A051087 A051081 * A107327 A162101 A128455

Adjacent sequences: A051090 A051091 A051092 * A051094 A051095 A051096

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Extended by R. J. Mathar, Oct 15 2008

Status

approved