A049545 Primes p such that x^13 = 2 has a solution mod p.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 59, 61, 67, 71, 73, 83, 89, 97, 101, 103, 107, 109, 113, 127, 137, 139, 149, 151, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293

Offset

1,1

Comments

Complement of A059245 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

0^13 == 2 (mod 2). 2^13 == 2 (mod 3). 2^13 == 2 (mod 5). 2^13 == 2 (mod 7). 7^13 == 2 (mod 11). 2^13 == 2 (mod 13). 15^13 == 2 (mod 17). 14^13 == 2 (mod 19). 18^13 == 2 (mod 23). 14^13 == 2 (mod 29). 4^13 == 2 (mod 31). 20^13 == 2 (mod 37). 36^13 == 2 (mod 41). 22^13 == 2 (mod 43). - R. J. Mathar, Jul 20 2025

Mathematica

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

Prog

(Magma) [p: p in PrimesUpTo(400) | exists(t){x : x in ResidueClassRing(p) | x^13 eq 2}]; // Vincenzo Librandi, Sep 13 2012

Crossrefs

Cf. A000040, A059245.

Sequence in context: A080191 A073350 A167773 * A127566 A103146 A329191

Adjacent sequences: A049542 A049543 A049544 * A049546 A049547 A049548

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved