A049544 Primes p such that x^12 = 2 has a solution mod p.

2, 23, 31, 47, 71, 89, 113, 127, 167, 191, 223, 233, 239, 257, 263, 281, 311, 353, 359, 383, 431, 439, 479, 503, 593, 599, 601, 617, 647, 719, 727, 743, 839, 863, 881, 887, 911, 919, 983, 1031, 1049, 1097, 1103, 1151, 1193, 1217, 1223, 1289, 1319, 1327

Offset

1,1

Comments

Complement of A059264 relative to A000040. - Vincenzo Librandi, Sep 13 2012

Links

R. J. Mathar, Table of n, a(n) for n = 1..1000

Index entries for related sequences

Example

0^12 == 2 (mod 2). 2^12 == 2 (mod 23). 8^12 == 2 (mod 31). 4^12 == 2 (mod 47). 8^12 == 2 (mod 71). 2^12 == 2 (mod 89). 3^12 == 2 (mod 113). 8^12 == 2 (mod 127). - R. J. Mathar, Jul 20 2025

Mathematica

ok[p_]:= Reduce[Mod[x^12- 2, p] == 0, x, Integers]=!=False; Select[Prime[Range[200]], ok] (* Vincenzo Librandi, Sep 13 2012 *)

Prog

(Magma) [p: p in PrimesUpTo(1400) | exists(t){x : x in ResidueClassRing(p) | x^12 eq 2}]; // Vincenzo Librandi, Sep 13 2012

Crossrefs

Cf. A000040, A059264.

Sequence in context: A053232 A065987 A107153 * A049568 A049556 A049580

Adjacent sequences: A049541 A049542 A049543 * A049545 A049546 A049547

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved