A049552 Primes p such that x^20 = 2 has a solution mod p.

2, 7, 23, 47, 73, 79, 89, 103, 113, 127, 151, 167, 199, 223, 233, 239, 257, 263, 337, 353, 359, 367, 383, 431, 439, 463, 479, 487, 503, 577, 593, 599, 607, 617, 647, 719, 727, 743, 823, 839, 863, 887, 911, 919, 937, 967, 983, 1033, 1039, 1049, 1063, 1087

Offset

1,1

Comments

Complement of A059309 relative to A000040. - Vincenzo Librandi, Sep 13 2012

Links

R. J. Mathar, Table of n, a(n) for n = 1..1000

Index entries for related sequences

Example

0^20 == 2 (mod 2). 3^20 == 2 (mod 7). 9^20 == 2 (mod 23). 9^20 == 2 (mod 47). 12^20 == 2 (mod 73). 4^20 == 2 (mod 79). 20^20 == 2 (mod 89). 21^20 == 2 (mod 103). - R. J. Mathar, Jul 20 2025

Mathematica

ok[p_]:= Reduce[Mod[x^20 - 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[200]], ok] (* Vincenzo Librandi, Sep 13 2012 *)

Prog

(Magma) [p: p in PrimesUpTo(1100) | exists(t){x : x in ResidueClassRing(p) | x^20 eq 2}]; // Vincenzo Librandi, Sep 13 2012

Crossrefs

Cf. A000040, A059309.

Sequence in context: A089176 A049232 A100917 * A049572 A094786 A028871

Adjacent sequences: A049549 A049550 A049551 * A049553 A049554 A049555

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved