A049596 Primes p such that x^9 = 2 has a solution mod p.

2, 3, 5, 11, 17, 23, 29, 31, 41, 43, 47, 53, 59, 71, 83, 89, 101, 107, 113, 127, 131, 137, 149, 157, 167, 173, 179, 191, 197, 223, 227, 229, 233, 239, 251, 257, 263, 269, 277, 281, 283, 293, 311, 317, 347, 353, 359, 383, 389, 397, 401, 419, 431, 439, 443, 449

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Coincides with sequence of "primes p such that x^27 = 2 has a solution mod p" for first 339 terms, then diverges.

Complement of A059262 relative to A000040. - Vincenzo Librandi, Sep 15 2012

Examples

			0^9 == 2 (mod 2). 2^9 == 2 (mod 3). 2^9 == 2 (mod 5). 6^9 == 2 (mod 11). 2^9 == 2 (mod 17). 9^9 == 2 (mod 23). 11^9 == 2 (mod 29). 16^9 == 2 (mod 31). 20^9 == 2 (mod 41). 26^9 == 2 (mod 43). - _R. J. Mathar_, Jul 20 2025
		

Links

• R. J. Mathar, Table of n, a(n) for n = 1..1000
• Index entries for related sequences

Crossrefs

Cf. A000040, A001132, A059262.

Programs

Magma

[p: p in PrimesUpTo(500) | exists(t){x : x in ResidueClassRing(p) | x^9 eq 2}]; // Vincenzo Librandi, Sep 15 2012

Mathematica

ok[p_]:= Reduce[Mod[x^9 - 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[100]], ok] (* Vincenzo Librandi, Sep 15 2012 *)