A216739 - OEIS

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A216739

Primes p such that x^16 = -2 has no solution mod p.

5, 7, 13, 17, 23, 29, 31, 37, 41, 47, 53, 61, 71, 73, 79, 89, 97, 101, 103, 109, 113, 127, 137, 149, 151, 157, 167, 173, 181, 191, 193, 197, 199, 223, 229, 233, 239, 241, 263, 269, 271, 277, 293, 311, 313, 317, 337, 349, 353, 359, 367, 373, 383, 389, 397

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OFFSET

1,1

COMMENTS

Complement of A051077 relative to A000040.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

MATHEMATICA

ok[p_] := Reduce[Mod[x^16 + 2, p] == 0, x, Integers] == False; Select[Prime[Range[100]], ok]

PROG

(Magma) [p: p in PrimesUpTo(400) | forall{x: x in ResidueClassRing(p) | x^16 ne -2}]; // Bruno Berselli, Sep 20 2012

(PARI) select(x->!ispower(Mod(-2, x), 16), primes(100)) \\ Michel Marcus, Mar 19 2023