A040038 Primes p such that x^3 = 3 has no solution mod p.

7, 13, 19, 31, 37, 43, 79, 97, 109, 127, 139, 157, 163, 181, 199, 211, 223, 229, 241, 277, 283, 313, 331, 337, 349, 373, 379, 397, 409, 421, 433, 457, 463, 487, 541, 571, 601, 607, 631, 673, 691, 709, 733, 739

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Primes of the form 7x^2+3xy+9y^2, whose discriminant is -243. - T. D. Noe, May 17 2005

Complement of A040036 relative to A000040. - Vincenzo Librandi, Sep 17 2012

Links

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

Programs

Magma

[p: p in PrimesUpTo(1000) | not exists{x : x in ResidueClassRing(p) | x^3 eq 3} ]; // Vincenzo Librandi, Sep 17 2012

Mathematica

ok[p_]:= Reduce[Mod[x^3 - 3, p] == 0, x, Integers] == False;Select[Prime[Range[200]], ok] (* Vincenzo Librandi, Sep 17 2012  *)

PARI

forprime(p=2,10^3,if(#polrootsmod(x^3-3,p)==0,print1(p,", "))) \\ Joerg Arndt, Jul 16 2015