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Primes p such that x^33 = 2 has no solution mod p.
2

%I #9 Sep 08 2022 08:45:02

%S 7,13,19,23,37,61,67,73,79,89,97,103,139,151,163,181,193,199,211,241,

%T 271,313,331,337,349,353,367,373,379,397,409,419,421,463,487,523,541,

%U 547,571,577,607,613,617,619,631,661,673,683,709,727,751,757,769,787

%N Primes p such that x^33 = 2 has no solution mod p.

%C Complement of A049565 relative to A000040.

%H Vincenzo Librandi, <a href="/A059335/b059335.txt">Table of n, a(n) for n = 1..1000</a>

%t ok[p_] := Reduce[Mod[x^33 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[150]], ok ] (* _Vincenzo Librandi_, Sep 20 2012 *)

%o (Magma) [p: p in PrimesUpTo(800) | not exists{x : x in ResidueClassRing(p) | x^33 eq 2 }]; // _Vincenzo Librandi_, Sep 20 2012

%Y A000040, A049565.

%K nonn,easy

%O 1,1

%A _Klaus Brockhaus_, Jan 26 2001