A049558 Primes p such that x^26 = 2 has a solution mod p.
2, 7, 17, 23, 31, 41, 47, 71, 73, 89, 97, 103, 113, 127, 137, 151, 167, 191, 193, 199, 223, 233, 239, 241, 257, 263, 271, 281, 311, 337, 353, 359, 367, 383, 401, 409, 431, 433, 439, 449, 457, 463, 479, 487, 503, 569, 577, 593, 601, 607, 617, 631, 641, 647
Offset: 1
Examples
0^26 == 2 (mod 2). 3^26 == 2 (mod 7). 7^26 == 2 (mod 17). 8^26 == 2 (mod 23). 2^26 == 2 (mod 31). 6^26 == 2 (mod 41). 21^26 == 2 (mod 47). 31^26 == 2 (mod 71). 36^26 == 2 (mod 73). 8^26 == 2 (mod 89). - _R. J. Mathar_, Jul 20 2025
Links
Programs
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Magma
[p: p in PrimesUpTo(700) | exists(t){x : x in ResidueClassRing(p) | x^26 eq 2}]; // Vincenzo Librandi, Sep 14 2012 -
Mathematica
ok[p_]:= Reduce[Mod[x^26 - 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[150]], ok] (* Vincenzo Librandi, Sep 14 2012 *)
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