A049547 Primes p such that x^15 = 2 has a solution mod p.

2, 3, 5, 17, 23, 29, 43, 47, 53, 59, 83, 89, 107, 109, 113, 127, 137, 149, 157, 167, 173, 179, 197, 223, 227, 229, 233, 239, 251, 257, 263, 269, 277, 283, 293, 307, 317, 347, 353, 359, 383, 389, 397, 419, 431, 433, 439, 443, 449, 457, 467, 479, 499, 503, 509

Offset

1,1

Comments

Complement of A059308 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

0^15 == 2 (mod 2). 2^15 == 2 (mod 3). 3^15 == 2 (mod 5). 9^15 == 2 (mod 17). 8^15 == 2 (mod 23). 27^15 == 2 (mod 29). 2^15 == 2 (mod 43). 6^15 == 2 (mod 47). 22^15 == 2 (mod 53). 55^15 == 2 (mod 59). 56^15 == 2 (mod 83). 8^15 == 2 (mod 89). 51^15 == 2 (mod 107).  - R. J. Mathar, Jul 20 2025

Mathematica

ok[p_]:= Reduce[Mod[x^15- 2, p] == 0, x, Integers]=!=False; Select[Prime[Range[200]], ok] (* Vincenzo Librandi, Sep 13 2012 *)

Prog

(Magma) [p: p in PrimesUpTo(600) | exists(t){x : x in ResidueClassRing(p) | x^15 eq 2}]; // Vincenzo Librandi, Sep 13 2012

Crossrefs

Cf. A000040, A059308.

Sequence in context: A119405 A032733 A111632 * A049577 A353153 A121558

Adjacent sequences: A049544 A049545 A049546 * A049548 A049549 A049550

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved