A045318 Primes p such that x^8 = 3 has no solution mod p.

5, 7, 17, 19, 29, 31, 37, 41, 43, 53, 61, 67, 73, 79, 89, 97, 101, 103, 113, 127, 137, 139, 149, 151, 157, 163, 173, 193, 197, 199, 211, 223, 233, 241, 257, 269, 271, 281, 283, 293, 307, 317, 331, 337, 349, 353, 367, 373, 379, 389, 397

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Complement of A045317 relative to A000040. - Vincenzo Librandi, Sep 19 2012

Links

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

Crossrefs

Cf. A000040, A045317, A301916, A320481.

Programs

Magma

[p: p in PrimesUpTo(500) | not exists{x : x in ResidueClassRing(p) | x^8 eq 3} ]; // Vincenzo Librandi, Sep 19 2012

Mathematica

ok[p_]:= Reduce[Mod[x^8 - 3, p] == 0, x, Integers] == False; Select[Prime[Range[200]], ok] (* Vincenzo Librandi, Sep 19 2012 *)