A049568 Primes p such that x^36 = 2 has a solution mod p.

2, 23, 31, 47, 71, 89, 113, 127, 167, 191, 223, 233, 239, 257, 263, 281, 311, 353, 359, 383, 431, 439, 479, 503, 593, 599, 601, 617, 647, 719, 727, 743, 839, 863, 881, 887, 911, 983, 1031, 1049, 1097, 1103, 1151, 1193, 1217, 1223, 1289, 1319, 1327, 1367

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Examples

			^36 == 2 (mod 2). 7^36 == 2 (mod 23). 2^36 == 2 (mod 31). 18^36 == 2 (mod 47). 2^36 == 2 (mod 71). 10^36 == 2 (mod 89). 33^36 == 2 (mod 113). 2^36 == 2 (mod 127). 40^36 == 2 (mod 167). - _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.

Programs

Magma

[p: p in PrimesUpTo(1500) | exists(t){x : x in ResidueClassRing(p) | x^36 eq 2}]; // Vincenzo Librandi, Sep 14 2012

Mathematica

ok[p_]:= Reduce[Mod[x^36 - 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[300]], ok] (* Vincenzo Librandi, Sep 14 2012 *)