A049543 Primes p such that x^11 = 2 has a solution mod p.

2, 3, 5, 7, 11, 13, 17, 19, 29, 31, 37, 41, 43, 47, 53, 59, 61, 71, 73, 79, 83, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Examples

			0^11 == 2 (mod 2). 2^11 == 2 (mod 3). 3^11 == 2 (mod 5). 4^11 == 2 (mod 7). 2^11 == 2 (mod 11). 7^11 == 2 (mod 13). 8^11 == 2 (mod 17). 13^11 == 2 (mod 19). 10^11 == 2 (mod 29). - _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, A059241 (complement: x^11 = 2 has no solutions mod p).

Programs

Magma

[p: p in PrimesUpTo(400) | exists(t){x : x in ResidueClassRing(p) | x^11 eq 2}]; // Vincenzo Librandi, Sep 13 2012

Mathematica

ok[p_]:= Reduce[Mod[x^11- 2, p] == 0, x, Integers]=!=False; Select[Prime[Range[200]], ok] (* Vincenzo Librandi, Sep 13 2012 *)

PARI

forprime(p=2, 2000, if([]~!=polrootsmod(x^11+2, p), print1(p, ", "))); print();
/* Joerg Arndt, Jun 24 2012 */