A049566 Primes p such that x^34 = 2 has a solution mod p.

2, 7, 17, 23, 31, 41, 47, 71, 73, 79, 89, 97, 113, 127, 151, 167, 191, 193, 199, 223, 233, 241, 257, 263, 271, 281, 311, 313, 337, 353, 359, 367, 383, 401, 431, 433, 439, 449, 457, 463, 479, 487, 503, 521, 569, 577, 593, 599, 601, 607, 617, 631, 641, 673, 719

Offset

1,1

Comments

Complement of A059336 relative to A000040. - Vincenzo Librandi, Sep 14 2012

Links

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

Index entries for related sequences

Example

0^34 == 2 (mod 2). 2^34 == 2 (mod 7). 6^34 == 2 (mod 17). 2^34 == 2 (mod 23). 15^34 == 2 (mod 31). 19^34 == 2 (mod 41). 12^34 == 2 (mod 47). 35^34 == 2 (mod 71). 16^34 == 2 (mod 73). - R. J. Mathar, Jul 20 2025

Mathematica

ok[p_]:= Reduce[Mod[x^34 - 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[200]], ok] (* Vincenzo Librandi, Sep 14 2012 *)

Prog

(Magma) [p: p in PrimesUpTo(800) | exists(t){x : x in ResidueClassRing(p) | x^34 eq 2}]; // Vincenzo Librandi, Sep 14 2012

Crossrefs

Cf. A000040, A059336.

Sequence in context: A049594 A049590 A049570 * A049558 A049546 A049578

Adjacent sequences: A049563 A049564 A049565 * A049567 A049568 A049569

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved