A049589 Primes p such that x^57 = 2 has a solution mod p.

2, 3, 5, 11, 17, 23, 29, 31, 41, 43, 47, 53, 59, 71, 83, 89, 101, 107, 109, 113, 127, 131, 137, 149, 157, 167, 173, 179, 197, 223, 227, 233, 239, 251, 257, 263, 269, 277, 281, 283, 293, 307, 311, 317, 347, 353, 359, 383, 389, 397, 401, 431, 433, 439, 443, 449

Offset

1,1

Comments

Complement of A059643 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

Mathematica

ok[p_] := Reduce[Mod[x^57 - 2, p] == 0, x, Integers] == True; Select[Prime[Range[100]], ok] (* Vincenzo Librandi, Sep 14 2012 *)

Prog

(Magma) [p: p in PrimesUpTo(500) | exists(t){x : x in ResidueClassRing(p) | x^57 eq 2}]; // Vincenzo Librandi, Sep 14 2012
(PARI)
N=10^4;  default(primelimit, N);
ok(p, r, k)={ return ( (p==r) || (Mod(r, p)^((p-1)/gcd(k, p-1))==1) ); }
forprime(p=2, N, if (ok(p, 2, 57), print1(p, ", ")));
/* Joerg Arndt, Sep 21 2012 */

Crossrefs

Cf. A000040, A059643.

Sequence in context: A154755 A040095 A040028 * A049583 A049596 A049571

Adjacent sequences: A049586 A049587 A049588 * A049590 A049591 A049592

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved