A049557 - OEIS

A049557

Primes p such that x^25 = 2 has a solution mod p.

2, 3, 5, 7, 13, 17, 19, 23, 29, 37, 43, 47, 53, 59, 67, 73, 79, 83, 89, 97, 103, 107, 109, 113, 127, 137, 139, 149, 157, 163, 167, 173, 179, 193, 197, 199, 223, 227, 229, 233, 239, 241, 257, 263, 269, 277, 283, 293, 307, 313, 317, 337, 347, 349, 353, 359, 367

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Complement of A059313 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

0^25 == 2 (mod 2). 2^25 == 2 (mod 3). 2^25 == 2 (mod 5). 2^25 == 2 (mod 7). 2^25 == 2 (mod 13). 2^25 == 2 (mod 17). 3^25 == 2 (mod 19). 16^25 == 2 (mod 23). 19^25 == 2 (mod 29). 15^25 == 2 (mod 37). - R. J. Mathar, Jul 20 2025

MATHEMATICA

ok[p_]:= Reduce[Mod[x^25 - 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[100]], ok] (* Vincenzo Librandi, Sep 14 2012 *)

PROG

(Magma) [p: p in PrimesUpTo(400) | exists(t){x : x in ResidueClassRing(p) | x^25 eq 2}]; // Vincenzo Librandi, Sep 14 2012

CROSSREFS

Cf. A000040, A059313.

Sequence in context: A040159 A040171 A040974 * A042991 A162338 A339342

Adjacent sequences: A049554 A049555 A049556 * A049558 A049559 A049560

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved