A049578 Primes p such that x^46 = 2 has a solution mod p.

2, 7, 17, 23, 31, 41, 71, 73, 79, 89, 97, 103, 113, 127, 137, 151, 167, 191, 193, 199, 223, 233, 239, 241, 257, 263, 271, 281, 311, 313, 337, 353, 359, 367, 383, 401, 409, 431, 433, 439, 449, 457, 463, 479, 487, 503, 521, 569, 577, 593, 601, 607, 617, 631

Offset

1,1

Comments

Complement of A059638 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

0^46 == 2 (mod 2). 2^46 == 2 (mod 7). 3^46 == 2 (mod 17). 5^46 == 2 (mod 23). 2^46 == 2 (mod 31). 13^46 == 2 (mod 41). 3^46 == 2 (mod 71). - R. J. Mathar, Jul 20 2025

Mathematica

ok[p_]:= Reduce[Mod[x^46 - 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[120]], ok] (* Vincenzo Librandi, Sep 14 2012 *)

Prog

(Magma) [p: p in PrimesUpTo(650) | exists(t){x : x in ResidueClassRing(p) | x^46 eq 2}]; // Vincenzo Librandi, Sep 14 2012

Crossrefs

Cf. A000040, A059638.

Sequence in context: A049566 A049558 A049546 * A162574 A215823 A049542

Adjacent sequences: A049575 A049576 A049577 * A049579 A049580 A049581

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved