A049542 - OEIS

%I #23 Jul 20 2025 08:17:05

%S 2,7,17,23,47,73,79,89,97,103,113,127,137,151,167,193,199,223,233,239,

%T 241,257,263,313,337,353,359,367,383,409,431,433,439,449,457,463,479,

%U 487,503,569,577,593,599,607,617,641,647,673,719,727,743,769,809,823

%N Primes p such that x^10 = 2 has a solution mod p.

%C Complement of A059263 relative to A000040. - _Vincenzo Librandi_, Sep 13 2012

%H R. J. Mathar, <a href="/A049542/b049542.txt">Table of n, a(n) for n = 1..1000</a>

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

%e 0^10 == 2 (mod 2). 2^10 == 2 (mod 7). 7^10 == 2 (mod 17). 11^10 == 2 (mod 23). 13^10 == 2 (mod 47). 2^10 == 2 (mod 73). 16^10 == 2 (mod 79). 44^10 == 2 (mod 89). 29^10 == 2 (mod 97). - _R. J. Mathar_, Jul 20 2025

%t ok[p_]:= Reduce[Mod[x^10- 2, p] == 0, x, Integers]=!=False; Select[Prime[Range[200]], ok] (* _Vincenzo Librandi_, Sep 13 2012 *)

%o (PARI) /* see A040098 */

%o (Magma) [p: p in PrimesUpTo(1100) | exists(t){x : x in ResidueClassRing(p) | x^10 eq 2}]; // _Vincenzo Librandi_, Sep 13 2012

%Y Cf. A000040, A059263.

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_