A051073 Primes p such that x^8 = -2 has a solution mod p.

2, 3, 11, 19, 43, 59, 67, 83, 107, 131, 139, 163, 179, 211, 227, 251, 257, 281, 283, 307, 331, 337, 347, 379, 419, 443, 467, 491, 499, 523, 547, 563, 571, 587, 617, 619, 643, 659, 683, 691, 739, 787, 811, 827, 859, 881, 883, 907, 947, 971, 1019

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Complement of A216735 relative to A000040. - Vincenzo Librandi, Sep 16 2012

Links

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

Crossrefs

Cf. A000040, A216735.

Programs

Magma

[p: p in PrimesUpTo(1200) | exists(t){x : x in ResidueClassRing(p) | x^8 eq - 2}]; // Vincenzo Librandi, Sep 15 2012

Mathematica

ok[p_]:= Reduce[Mod[x^8 + 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[500]], ok] (* Vincenzo Librandi, Sep 15 2012 *)

PARI

forprime(p=2, 2000, if([]~!=polrootsmod(x^8+2, p), print1(p, ", "))); print();
/* Joerg Arndt, Jun 24 2012 */

Extensions

More terms from Joerg Arndt, Jun 24 2012