A049543 - OEIS

%I #21 Sep 08 2022 08:44:58

%S 2,3,5,7,11,13,17,19,29,31,37,41,43,47,53,59,61,71,73,79,83,97,101,

%T 103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,

%U 193,197,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293

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

%H R. J. Mathar, <a href="/A049543/b049543.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Pri#smp">Index entries for related sequences</a>

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

%o (PARI)

%o forprime(p=2, 2000, if([]~!=polrootsmod(x^11+2, p), print1(p, ", "))); print();

%o /* _Joerg Arndt_, Jun 24 2012 */

%o (Magma) [p: p in PrimesUpTo(400) | exists(t){x : x in ResidueClassRing(p) | x^11 eq 2}]; // _Vincenzo Librandi_, Sep 13 2012

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

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_