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Primes p such that x^44 = -2 has no solution mod p.
2

%I #8 Sep 08 2022 08:46:03

%S 5,7,13,17,23,29,31,37,41,47,53,61,67,71,79,89,97,101,103,109,127,137,

%T 149,151,157,167,173,181,191,193,197,199,223,229,239,241,263,269,271,

%U 277,293,311,313,317,349,353,359,367,373,383,389,397,401,409,419

%N Primes p such that x^44 = -2 has no solution mod p.

%C Complement of A051091 relative to A000040.

%H Vincenzo Librandi, <a href="/A216753/b216753.txt">Table of n, a(n) for n = 1..1000</a>

%t ok[p_] := Reduce[Mod[x^44 + 2, p] == 0, x, Integers] == False;Select[Prime[Range[200]], ok]

%o (Magma) [p: p in PrimesUpTo(500) | not exists{x: x in ResidueClassRing(p) | x^44 eq -2}];

%Y Cf. A000040, A051091.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Sep 16 2012