A049582 Primes p such that x^50 = 2 has a solution mod p.

2, 7, 17, 23, 47, 73, 79, 89, 97, 103, 113, 127, 137, 167, 193, 199, 223, 233, 239, 241, 257, 263, 313, 337, 353, 359, 367, 383, 409, 431, 433, 439, 449, 457, 463, 479, 487, 503, 569, 577, 593, 599, 607, 617, 641, 647, 673, 719, 727, 743, 769, 809, 823, 839

Offset

1,1

Comments

Complement of A059639 relative to A000040. - Vincenzo Librandi, Sep 14 2012

Links

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

Index entries for related sequences

Example

0^50 == 2 (mod 2). 3^50 == 2 (mod 7). 6^50 == 2 (mod 17). 4^50 == 2 (mod 23). 17^50 == 2 (mod 47). 4^50 == 2 (mod 73). 29^50 == 2 (mod 79). - R. J. Mathar, Jul 20 2025

Mathematica

ok[p_]:= Reduce[Mod[x^50 - 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[200]], ok] (* Vincenzo Librandi, Sep 14 2012 *)

Prog

(Magma) [p: p in PrimesUpTo(900) | exists(t){x : x in ResidueClassRing(p) | x^50 eq 2}]; // Vincenzo Librandi, Sep 14 2012

Crossrefs

Cf. A000040, A059639.

Sequence in context: A162574 A215823 A049542 * A220273 A276698 A386373

Adjacent sequences: A049579 A049580 A049581 * A049583 A049584 A049585

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved