A049549 Primes p such that x^17 = 2 has a solution mod p.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 107, 109, 113, 127, 131, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 241, 251, 257, 263, 269, 271, 277, 281, 283

Offset

1,1

Comments

Complement of A058999 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

0^17 == 2 (mod 2). 2^17 == 2 (mod 3). 2^17 == 2 (mod 5). 4^17 == 2 (mod 7). 8^17 == 2 (mod 11). 6^17 == 2 (mod 13). 2^17 == 2 (mod 17). 10^17 == 2 (mod 19). 4^17 == 2 (mod 23). 3^17 == 2 (mod 29). 8^17 == 2 (mod 31). 18^17 == 2 (mod 37). 33^17 == 2 (mod 41). 32^17 == 2 (mod 43). - R. J. Mathar, Jul 20 2025

Mathematica

ok[p_]:= Reduce[Mod[x^17- 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^17 eq 2}]; // Vincenzo Librandi, Sep 13 2012

Crossrefs

Cf. A000040, A058999.

Sequence in context: A164837 A069675 A049585 * A030291 A242541 A052085

Adjacent sequences: A049546 A049547 A049548 * A049550 A049551 A049552

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved