A216735 Primes p such that x^8 = -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, 349, 353, 359, 367, 373, 383, 389, 397, 401, 409, 421, 431

Offset: 1

Author

Vincenzo Librandi, Sep 15 2012

Keywords

• nonn
• easy

Comments

Complement of A051073 relative to A000040.

Links

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

Crossrefs

Cf. A000040, A051073.

Programs

Magma

[p: p in PrimesUpTo(500) | forall{x: x in ResidueClassRing(p) | x^8 ne -2}]; // Bruno Berselli, Sep 20 2012

Mathematica

ok[p_] := Reduce[Mod[x^8 + 2, p] == 0, x, Integers] == False; Select[Prime[Range[100]], ok]

PARI

select(x->!ispower(Mod(-2, x), 8), primes(100)) \\ Michel Marcus, Mar 19 2023