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Primes p such that x^26 = 2 has no solution mod p.
2

%I #8 Sep 08 2022 08:45:02

%S 3,5,11,13,19,29,37,43,53,59,61,67,79,83,101,107,109,131,139,149,157,

%T 163,173,179,181,197,211,227,229,251,269,277,283,293,307,313,317,331,

%U 347,349,373,379,389,397,419,421,443,461,467,491,499,509,521,523,541

%N Primes p such that x^26 = 2 has no solution mod p.

%C Complement of A049558 relative to A000040.

%H Vincenzo Librandi, <a href="/A059314/b059314.txt">Table of n, a(n) for n = 1..1000</a>

%t ok[p_] := Reduce[Mod[x^26 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[100]], ok ] (* _Vincenzo Librandi_, Sep 20 2012 *)

%o (Magma) [p: p in PrimesUpTo(550) | not exists{x : x in ResidueClassRing(p) | x^26 eq 2 }]; // _Vincenzo Librandi_, Sep 20 2012

%K nonn,easy

%O 1,1

%A _Klaus Brockhaus_, Jan 25 2001