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Primes p such that x^43 = 2 has no solution mod p.
2

%I #7 Sep 08 2022 08:45:02

%S 173,431,947,1033,1291,1549,1721,1979,2237,2753,3011,3527,3613,4129,

%T 4817,4903,5333,5591,5849,6451,6709,6967,7741,8171,8429,9203,9461,

%U 9547,9719,10321,10837,11353,11783,12041,13159,13331,13417,13933,14621

%N Primes p such that x^43 = 2 has no solution mod p.

%C Complement of A058853 relative to A000040.

%H Vincenzo Librandi, <a href="/A059243/b059243.txt">Table of n, a(n) for n = 1..1000</a>

%t ok[p_]:= Reduce[Mod[x^43 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[4000]], ok] (* _Vincenzo Librandi_, Sep 20 2012 *)

%o (Magma) [p: p in PrimesUpTo(15000) | not exists{x : x in ResidueClassRing(p) | x^43 eq 2} ]; // _Vincenzo Librandi_, Sep 20 2012

%Y Cf. A000040, A058853.

%K easy,nonn

%O 1,1

%A _Klaus Brockhaus_, Jan 21 2001