A040160 Primes p such that x^5 = 2 has no solution mod p.

11, 31, 41, 61, 71, 101, 131, 181, 191, 211, 271, 281, 311, 331, 401, 421, 461, 491, 521, 541, 601, 631, 661, 691, 701, 751, 761, 811, 821, 881, 941, 991, 1021, 1031, 1051, 1061, 1091, 1151, 1171, 1201, 1231, 1291, 1301, 1321, 1361, 1381, 1451, 1471, 1481, 1511, 1531, 1571

Offset

1,1

Comments

Complement of A040159 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 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[300]], ok] (* Vincenzo Librandi, Sep 18 2012  *)

Prog

(Magma) [p: p in PrimesUpTo(1300) | forall{x: x in ResidueClassRing(p) | x^5 ne 2}]; // Bruno Berselli, Sep 12 2012
(Magma) [p: p in PrimesUpTo(1500) | not exists{x : x in ResidueClassRing(p) | x^5 eq 2} ]; // Vincenzo Librandi, Sep 18 2012
(PARI) forprime(p=2, 10^3, if(#polrootsmod(x^5-2, p)==0, print1(p, ", "))) \\ Joerg Arndt, Jul 16 2015

Crossrefs

Sequence in context: A040975 A188384 A040172 * A040981 A181603 A040983

Adjacent sequences: A040157 A040158 A040159 * A040161 A040162 A040163

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved