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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Complement of A059349 relative to A000040. - Vincenzo Librandi, Sep 14 2012

Examples

			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
		

Links

• R. J. Mathar, Table of n, a(n) for n = 1..1000
• Index entries for related sequences

Crossrefs

Cf. A000040, A059349.

Programs

Magma

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

Mathematica

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