A045317 Primes p such that x^8 = 3 has a solution mod p.

2, 3, 11, 13, 23, 47, 59, 71, 83, 107, 109, 131, 167, 179, 181, 191, 227, 229, 239, 251, 263, 277, 311, 313, 347, 359, 383, 419, 421, 431, 433, 443, 467, 479, 491, 503, 541, 563, 587, 599, 601, 647, 659, 683, 709

Offset

1,1

Comments

Complement of A045318 relative to A000040. - Vincenzo Librandi, Sep 13 2012

Links

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

Mathematica

ok[p_]:= Reduce[Mod[x^8- 3, p] == 0, x, Integers]=!=False; Select[Prime[Range[200]], ok] (* Vincenzo Librandi, Sep 13 2012 *)

Prog

(Magma) [p: p in PrimesUpTo(800) | exists(t){x : x in ResidueClassRing(p) | x^8 eq 3}]; // Vincenzo Librandi, Sep 13 2012
(PARI) isok(p) = isprime(p) && ispower(Mod(3, p), 8); \\ Michel Marcus, Oct 17 2018

Crossrefs

Cf. A000040, A045318.

Sequence in context: A164624 A215819 A040101 * A215378 A078763 A157884

Adjacent sequences: A045314 A045315 A045316 * A045318 A045319 A045320

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved