A051096 Primes p such that x^54 = -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, 347, 353, 401, 419, 443, 449, 457, 467, 491, 499, 521, 563, 569, 587, 593, 601, 617, 641, 643, 659, 683, 691, 761, 809, 827, 857, 881, 929, 947, 953, 971, 977, 1019, 1049, 1051, 1091, 1097, 1163

Offset

1,1

Comments

Complement of A216772 relative to A000040. - Vincenzo Librandi, Sep 17 2012

Links

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

Mathematica

ok[p_]:= Reduce[Mod[x^54 + 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[300]], ok] (* Vincenzo Librandi, Sep 16 2012 *)

Prog

(PARI)
forprime(p=2, 2000, if([]~!=polrootsmod(x^54+2, p), print1(p, ", "))); print();
/* Joerg Arndt, Jun 24 2012 */
(Magma) [p: p in PrimesUpTo(1200) | exists(t){x : x in ResidueClassRing(p) | x^54 eq - 2}]; // Vincenzo Librandi, Sep 16 2012

Crossrefs

Sequence in context: A024597 A147655 A051072 * A051078 A051090 A263933

Adjacent sequences: A051093 A051094 A051095 * A051097 A051098 A051099

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Joerg Arndt, Jul 27 2011

Status

approved