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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

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

Links

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

Programs

Magma

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

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 *)

PARI

/* see A051071 */

Extensions

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