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

%I #10 Sep 08 2022 08:46:03

%S 5,7,13,23,29,31,37,47,53,61,71,79,101,103,109,127,131,149,151,157,

%T 167,173,181,191,197,199,223,229,239,263,269,271,277,293,311,313,317,

%U 349,359,367,373,383,389,397,421,431,439,443,461,463,479,487,503,509,521,541

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

%C Complement of A051082 relative to A000040.

%H Vincenzo Librandi, <a href="/A216744/b216744.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[110]], ok]

%o (Magma) [ p: p in PrimesUpTo(600) | not exists{x : x in ResidueClassRing(p) | x^26 eq -2} ]; // _Vincenzo Librandi_, Sep 16 2012

%Y Cf. A000040, A051082.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Sep 15 2012