A051072 Primes p such that x^6 = -2 has a solution mod p.

2, 3, 11, 17, 41, 43, 59, 83, 89, 107, 113, 131, 137, 179, 227, 233, 251, 257, 281, 283, 307, 347, 353, 401, 419, 433, 443, 449, 457, 467, 491, 499, 521, 563, 569, 587, 593, 601, 617, 641, 643, 659, 683, 691, 739, 761, 809, 811, 827, 857, 881, 929, 947, 953, 971, 977, 1019

Offset

1,1

Comments

Complement of A216734 relative to A000040. - Vincenzo Librandi, Sep 16 2012

Links

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

Mathematica

ok[p_]:= Reduce[Mod[x^6 + 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[500]], ok] (* Vincenzo Librandi, Sep 15 2012 *)

Prog

(PARI)
forprime(p=2, 2000, if([]~!=polrootsmod(x^6+2, p), print1(p, ", "))); print();
/* Joerg Arndt, Jun 24 2012 */
(Magma) [p: p in PrimesUpTo(1200) | exists(t){x : x in ResidueClassRing(p) | x^6 eq - 2}]; // Vincenzo Librandi, Sep 15 2012

Crossrefs

Sequence in context: A025099 A024597 A147655 * A051096 A051078 A051090

Adjacent sequences: A051069 A051070 A051071 * A051073 A051074 A051075

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Joerg Arndt, Jul 27 2011

Status

approved