A049564 Primes p such that x^32 = 2 has a solution mod p.

2, 7, 23, 31, 47, 71, 73, 79, 89, 103, 127, 151, 167, 191, 199, 223, 233, 239, 263, 271, 311, 337, 359, 367, 383, 431, 439, 463, 479, 487, 503, 599, 601, 607, 631, 647, 719, 727, 743, 751, 823, 839, 863, 881, 887, 911, 919, 937, 967, 983, 991, 1031, 1039

Offset

1,1

Comments

Complement of A059349 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

0^32 == 2 (mod 2). 3^32 == 2 (mod 7). 11^32 == 2 (mod 23). 8^32 == 2 (mod 31). 22^32 == 2 (mod 47). 29^32 == 2 (mod 71). 4^32 == 2 (mod 73). 6^32 == 2 (mod 79). 6^32 == 2 (mod 89). - R. J. Mathar, Jul 20 2025

Mathematica

ok[p_]:= Reduce[Mod[x^32 - 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[300]], ok] (* Vincenzo Librandi, Sep 14 2012 *)

Prog

(Magma) [p: p in PrimesUpTo(1100) | exists(t){x : x in ResidueClassRing(p) | x^32 eq 2}]; // Vincenzo Librandi, Sep 14 2012

Crossrefs

Cf. A000040, A059349.

Sequence in context: A040098 A045315 A072935 * A072936 A049584 A045382

Adjacent sequences: A049561 A049562 A049563 * A049565 A049566 A049567

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved