A040162 Primes p such that x^5 = 3 has no solution mod p.

11, 31, 61, 71, 101, 131, 151, 181, 191, 211, 241, 251, 271, 281, 311, 331, 401, 421, 461, 521, 541, 571, 601, 631, 641, 691, 701, 751, 811, 821, 881, 911, 941, 971, 991, 1031, 1061, 1151, 1181, 1201, 1231, 1291, 1301, 1321, 1361, 1381, 1451, 1481, 1531

Offset

1,1

Comments

Complement of A040161 relative to A000040. - Vincenzo Librandi, Sep 18 2012

Links

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

Mathematica

ok[p_]:= Reduce[Mod[x^5 - 3, p] == 0, x, Integers] == False; Select[Prime[Range[300]], ok] (* Vincenzo Librandi, Sep 18 2012  *)

Prog

(Magma) [ p: p in PrimesUpTo(1600) | forall(t){x : x in ResidueClassRing(p) | x^5 ne 3} ]; // Klaus Brockhaus, Jun 03 2009
(Magma) [p: p in PrimesUpTo(1550) | not exists{x : x in ResidueClassRing(p) | x^5 eq 3} ]; // Vincenzo Librandi, Sep 18 2012

Crossrefs

Cf. A040161 (primes p such that x^5 = 3 has a solution mod p).

Sequence in context: A028877 A087394 A196117 * A113747 A202007 A125239

Adjacent sequences: A040159 A040160 A040161 * A040163 A040164 A040165

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Klaus Brockhaus, Jun 03 2009

Status

approved