A059644 Primes p such that x^58 = 2 has no solution mod p.

3, 5, 11, 13, 19, 29, 37, 43, 53, 59, 61, 67, 83, 101, 107, 109, 131, 139, 149, 157, 163, 173, 179, 181, 197, 211, 227, 229, 233, 251, 269, 277, 283, 293, 307, 317, 331, 347, 349, 373, 379, 389, 397, 419, 421, 443, 461, 467, 491, 499, 509, 523, 541, 547, 557

Offset

1,1

Comments

Complement of A049590 relative to A000040.

Links

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

Mathematica

ok[p_] := Reduce[Mod[x^58 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[120]], ok] (* Vincenzo Librandi, Sep 21 2012 *)

Prog

(Magma) [p: p in PrimesUpTo(600) | not exists{x: x in ResidueClassRing(p) | x^58 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, 58), print1(p, ", ")));
/* Joerg Arndt, Sep 21 2012 */

Crossrefs

Cf. A000040, A049590.

Sequence in context: A059314 A059336 A059350 * A059646 A319041 A003629

Adjacent sequences: A059641 A059642 A059643 * A059645 A059646 A059647

Keyword

nonn,easy

Author

Klaus Brockhaus, Feb 02 2001

Status

approved