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Primes p such that x^42 = -2 has no solution mod p.
2

%I #7 Sep 08 2022 08:46:03

%S 5,7,13,19,23,29,31,37,43,47,53,61,67,71,73,79,97,101,103,109,113,127,

%T 139,149,151,157,163,167,173,181,191,193,197,199,211,223,229,239,241,

%U 263,269,271,277,281,293,311,313,317,331,337,349,359,367,373,379,383

%N Primes p such that x^42 = -2 has no solution mod p.

%C Complement of A051090 relative to A000040.

%H Vincenzo Librandi, <a href="/A216752/b216752.txt">Table of n, a(n) for n = 1..1000</a>

%t ok[p_]:=Reduce[Mod[x^42 + 2, p] == 0, x, Integers] == False;Select[Prime[Range[300]], ok] (* _Vincenzo Librandi_, Sep 16 2012 *)

%o (Magma) [p: p in PrimesUpTo(500) | not exists{x : x in ResidueClassRing(p) | x^42 eq -2} ];

%Y Cf. A000040, A051090.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Sep 16 2012