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Primes p such that x^28 = -2 has no solution mod p.
2

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

%S 5,7,13,17,23,29,31,37,41,43,47,53,61,71,79,97,101,103,109,113,127,

%T 137,149,151,157,167,173,181,191,193,197,199,211,223,229,239,241,263,

%U 269,271,277,281,293,311,313,317,337,349,359,367,373,379,383,389,397,401,409,421,431,433

%N Primes p such that x^28 = -2 has no solution mod p.

%C Complement of A051083 relative to A000040.

%H Vincenzo Librandi, <a href="/A216745/b216745.txt">Table of n, a(n) for n = 1..1000</a>

%t ok[p_]:= Reduce[Mod[x^28 + 2, p] == 0, x, Integers] == False; Select[Prime[Range[110]], ok]

%o (Magma) [p: p in PrimesUpTo(500) | not exists{x : x in ResidueClassRing(p) | x^28 eq -2} ]; // _Vincenzo Librandi_, Sep 16 2012

%Y Cf. A000040, A051083.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Sep 15 2012