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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Complement of A040159 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(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

Mathematica

ok[p_]:= Reduce[Mod[x^5 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[300]], ok] (* 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