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Primes p such that x^50 = 2 has no solution mod p.
2

%I #12 Sep 08 2022 08:45:03

%S 3,5,11,13,19,29,31,37,41,43,53,59,61,67,71,83,101,107,109,131,139,

%T 149,151,157,163,173,179,181,191,197,211,227,229,251,269,271,277,281,

%U 283,293,307,311,317,331,347,349,373,379,389,397,401,419,421,443,461,467

%N Primes p such that x^50 = 2 has no solution mod p.

%C Complement of A049582 relative to A000040.

%H Vincenzo Librandi, <a href="/A059639/b059639.txt">Table of n, a(n) for n = 1..1000</a>

%t ok[p_] := Reduce[Mod[x^50 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[100]], ok] (* _Vincenzo Librandi_, Sep 21 2012 *)

%o (Magma) [p: p in PrimesUpTo(500) | not exists{x: x in ResidueClassRing(p) | x^50 eq 2}]; // _Vincenzo Librandi_, Sep 21 2012

%Y Cf. A000040, A049582.

%K nonn,easy

%O 1,1

%A _Klaus Brockhaus_, Feb 02 2001