A059643 Primes p such that x^57 = 2 has no solution mod p.

7, 13, 19, 37, 61, 67, 73, 79, 97, 103, 139, 151, 163, 181, 191, 193, 199, 211, 229, 241, 271, 313, 331, 337, 349, 367, 373, 379, 409, 419, 421, 457, 463, 487, 523, 541, 547, 571, 577, 607, 613, 619, 631, 647, 661, 673, 709, 751, 757, 761, 769, 787, 823, 829

Offset

1,1

Comments

Complement of A049589 relative to A000040.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Mathematica

ok[p_] := Reduce[Mod[x^57 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[200]], ok] (* Vincenzo Librandi, Sep 21 2012 *)

Prog

(Magma) [p: p in PrimesUpTo(900) | not exists{x: x in ResidueClassRing(p) | x^57 eq 2}]; // Vincenzo Librandi, Sep 21 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, A049589.

Sequence in context: A320532 A059262 A059640 * A040034 A176229 A266268

Adjacent sequences: A059640 A059641 A059642 * A059644 A059645 A059646

Keyword

nonn,easy

Author

Klaus Brockhaus, Feb 02 2001

Status

approved