A049546 Primes p such that x^14 = 2 has a solution mod p.

2, 7, 17, 23, 31, 41, 47, 73, 79, 89, 97, 103, 137, 151, 167, 191, 193, 199, 223, 233, 241, 257, 263, 271, 311, 313, 353, 359, 367, 383, 401, 409, 431, 433, 439, 457, 479, 487, 503, 521, 569, 577, 593, 599, 601, 607, 631, 641, 647, 673, 719, 727, 751, 761

Offset

1,1

Comments

Complement of A059265 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

0^14 == 2 (mod 2). 3^14 == 2 (mod 7). 3^14 == 2 (mod 17). 7^14 == 2 (mod 23). 15^14 == 2 (mod 31). 7^14 == 2 (mod 41). 15^14 == 2 (mod 47). 4^14 == 2 (mod 73). 31^14 == 2 (mod 79). - R. J. Mathar, Jul 20 2025

Mathematica

ok[p_]:= Reduce[Mod[x^14- 2, 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^14 eq 2}]; // Vincenzo Librandi, Sep 13 2012

Crossrefs

Cf. A000040, A059265.

Sequence in context: A049570 A049566 A049558 * A049578 A162574 A215823

Adjacent sequences: A049543 A049544 A049545 * A049547 A049548 A049549

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved