A049554 Primes p such that x^22 = 2 has a solution mod p.

2, 7, 17, 31, 41, 47, 71, 73, 79, 97, 103, 113, 127, 137, 151, 167, 191, 193, 223, 233, 239, 241, 257, 263, 271, 281, 311, 313, 337, 359, 367, 383, 401, 409, 431, 433, 439, 449, 457, 479, 487, 503, 521, 569, 577, 593, 599, 601, 607, 631, 641, 647, 673, 719

Offset

1,1

Comments

Complement of A059311 relative to A000040. - Vincenzo Librandi, Sep 14 2012

Links

R. J. Mathar, Table of n, a(n) for n = 1..1000

Index entries for related sequences

Example

0^22 == 2 (mod 2). 2^22 == 2 (mod 7). 5^22 == 2 (mod 17). 8^22 == 2 (mod 31). 11^22 == 2 (mod 41). 23^22 == 2 (mod 47). 28^22 == 2 (mod 71). 18^22 == 2 (mod 73). 34^22 == 2 (mod 79). 38^22 == 2 (mod 97). 25^22 == 2 (mod 103). 36^22 == 2 (mod 113). 2^22 == 2 (mod 127). - R. J. Mathar, Jul 20 2025

Mathematica

ok[p_]:= Reduce[Mod[x^22 - 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[150]], ok] (* Vincenzo Librandi, Sep 14 2012 *)

Prog

(Magma) [p: p in PrimesUpTo(800) | exists(t){x : x in ResidueClassRing(p) | x^22 eq 2}]; // Vincenzo Librandi, Sep 14 2012

Crossrefs

Cf. A000040, A059311.

Sequence in context: A019357 A024920 A091313 * A019398 A086513 A166381

Adjacent sequences: A049551 A049552 A049553 * A049555 A049556 A049557

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved