A049557 Primes p such that x^25 = 2 has a solution mod p.

2, 3, 5, 7, 13, 17, 19, 23, 29, 37, 43, 47, 53, 59, 67, 73, 79, 83, 89, 97, 103, 107, 109, 113, 127, 137, 139, 149, 157, 163, 167, 173, 179, 193, 197, 199, 223, 227, 229, 233, 239, 241, 257, 263, 269, 277, 283, 293, 307, 313, 317, 337, 347, 349, 353, 359, 367

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Complement of A059313 relative to A000040. - Vincenzo Librandi, Sep 14 2012

Examples

			0^25 == 2 (mod 2). 2^25 == 2 (mod 3). 2^25 == 2 (mod 5). 2^25 == 2 (mod 7). 2^25 == 2 (mod 13). 2^25 == 2 (mod 17). 3^25 == 2 (mod 19). 16^25 == 2 (mod 23). 19^25 == 2 (mod 29). 15^25 == 2 (mod 37). - _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, A059313.

Programs

Magma

[p: p in PrimesUpTo(400) | exists(t){x : x in ResidueClassRing(p) | x^25 eq 2}]; // Vincenzo Librandi, Sep 14 2012

Mathematica

ok[p_]:= Reduce[Mod[x^25 - 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[100]], ok]  (* Vincenzo Librandi, Sep 14 2012 *)