A040136 Primes p such that x^4 = 15 has no solution mod p.

13, 17, 19, 23, 29, 31, 37, 41, 47, 73, 79, 83, 89, 97, 101, 107, 139, 149, 151, 157, 167, 173, 193, 197, 199, 211, 227, 229, 233, 263, 269, 271, 277, 281, 293, 313, 331, 337, 347, 353, 373, 379, 383, 389, 397

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Complement of A040130 relative to A000040. - Vincenzo Librandi, Sep 18 2012

Links

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

Programs

Magma

[p: p in PrimesUpTo(500) | not exists{x : x in ResidueClassRing(p) | x^4 eq 15} ]; // Vincenzo Librandi, Sep 18 2012

Mathematica

ok[p_]:= Reduce[Mod[x^4 - 15, p] == 0, x, Integers] == False; Select[Prime[Range[100]], ok] (* Vincenzo Librandi, Sep 18 2012  *)

PARI

is(n)=isprime(n) && !ispower(Mod(15,n),4) \\ Charles R Greathouse IV, Feb 23 2017