|
%I #40 Sep 08 2022 08:44:55
%S 29,43,71,113,127,197,211,239,281,337,379,421,449,463,491,547,617,659,
%T 701,743,757,827,883,911,967,1009,1051,1093,1289,1303,1373,1429,1471,
%U 1499,1583,1597,1667,1723,1877,1933,2017,2087,2129,2213,2269,2297,2311,2339,2381,2423,2437,2521
%N Primes p such that x^7 = 2 has no solution mod p.
%C Complement of A042966 relative to A000040. Coincides for the first 96 terms with the sequence of primes p such that x^49 = 2 has no solution mod p (first divergence is at 4999, cf. A059667). - _Klaus Brockhaus_, Feb 04 2001
%H Vincenzo Librandi, <a href="/A042967/b042967.txt">Table of n, a(n) for n = 1..1000</a>
%e x^7 = 2 has no solution mod 29, so 29 is in the sequence.
%e 8^7 = 2097152 and (2097152 - 2)/31 = 67650, so 31 is not in the sequence.
%t sevPow2ModPQ[p_] := Reduce[Mod[x^7 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[700]], sevPow2ModPQ] (* _Vincenzo Librandi_, Sep 19 2012 *)
%o (Magma) [p: p in PrimesUpTo(3000) | forall{x: x in ResidueClassRing(p) | x^7 ne 2}]; // _Vincenzo Librandi_, Aug 21 2012
%o (Magma) [p: p in PrimesUpTo(2600) | not exists{x : x in ResidueClassRing(p) | x^7 eq 2} ]; // _Vincenzo Librandi_, Sep 19 2012
%Y Cf. A000040, A042966, A059667.
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_
|
