A049544 Primes p such that x^12 = 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, 919, 983, 1031, 1049, 1097, 1103, 1151, 1193, 1217, 1223, 1289, 1319, 1327
Offset: 1
Examples
0^12 == 2 (mod 2). 2^12 == 2 (mod 23). 8^12 == 2 (mod 31). 4^12 == 2 (mod 47). 8^12 == 2 (mod 71). 2^12 == 2 (mod 89). 3^12 == 2 (mod 113). 8^12 == 2 (mod 127). - _R. J. Mathar_, Jul 20 2025
Links
Programs
-
Magma
[p: p in PrimesUpTo(1400) | exists(t){x : x in ResidueClassRing(p) | x^12 eq 2}]; // Vincenzo Librandi, Sep 13 2012
-
Mathematica
ok[p_]:= Reduce[Mod[x^12- 2, p] == 0, x, Integers]=!=False; Select[Prime[Range[200]], ok] (* Vincenzo Librandi, Sep 13 2012 *)
Comments