A049542 Primes p such that x^10 = 2 has a solution mod p.

2, 7, 17, 23, 47, 73, 79, 89, 97, 103, 113, 127, 137, 151, 167, 193, 199, 223, 233, 239, 241, 257, 263, 313, 337, 353, 359, 367, 383, 409, 431, 433, 439, 449, 457, 463, 479, 487, 503, 569, 577, 593, 599, 607, 617, 641, 647, 673, 719, 727, 743, 769, 809, 823

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Complement of A059263 relative to A000040. - Vincenzo Librandi, Sep 13 2012

Examples

			0^10 == 2 (mod 2). 2^10 == 2 (mod 7). 7^10 == 2 (mod 17). 11^10 == 2 (mod 23). 13^10 == 2 (mod 47). 2^10 == 2 (mod 73). 16^10 == 2 (mod 79). 44^10 == 2 (mod 89). 29^10 == 2 (mod 97). - _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, A059263.

Programs

Magma

[p: p in PrimesUpTo(1100) | exists(t){x : x in ResidueClassRing(p) | x^10 eq 2}]; // Vincenzo Librandi, Sep 13 2012

Mathematica

ok[p_]:= Reduce[Mod[x^10- 2, p] == 0, x, Integers]=!=False; Select[Prime[Range[200]], ok] (* Vincenzo Librandi, Sep 13 2012 *)

PARI

/* see A040098 */