A051084 Primes p such that x^30 = -2 has a solution mod p.

2, 3, 17, 43, 59, 83, 89, 107, 113, 137, 179, 227, 233, 251, 257, 283, 307, 347, 353, 419, 433, 443, 449, 457, 467, 499, 563, 569, 587, 593, 617, 641, 643, 659, 683, 739, 809, 827, 857, 929, 947, 953, 971, 977, 1019, 1049, 1097, 1163, 1187, 1193, 1217, 1259, 1283, 1289, 1307, 1409

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Complement of A216746 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(1410) | exists(t){x : x in ResidueClassRing(p) | x^30 eq - 2}]; // Vincenzo Librandi, Sep 15 2012

Mathematica

ok[p_]:= Reduce[Mod[x^30 + 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[500]], ok] (* Vincenzo Librandi, Sep 15 2012 *)

PARI

/* see A051071 */

Extensions

More terms from Joerg Arndt, Jul 27 2011