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

1,1

Links

R. J. Mathar, Table of n, a(n) for n = 1..1000

Index entries for related sequences

Example

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

Mathematica

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

Prog

(PARI)
forprime(p=2, 2000, if([]~!=polrootsmod(x^11+2, p), print1(p, ", "))); print();
/* Joerg Arndt, Jun 24 2012 */
(Magma) [p: p in PrimesUpTo(400) | exists(t){x : x in ResidueClassRing(p) | x^11 eq 2}]; // Vincenzo Librandi, Sep 13 2012

Crossrefs

Cf. A000040, A059241 (complement: x^11 = 2 has no solutions mod p).

Sequence in context: A008792 A359497 A094746 * A294200 A109997 A174144

Adjacent sequences: A049540 A049541 A049542 * A049544 A049545 A049546

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved