A059641 Primes p such that x^52 = 2 has no solution mod p.

3, 5, 11, 13, 17, 19, 29, 37, 41, 43, 53, 59, 61, 67, 79, 83, 97, 101, 107, 109, 131, 137, 139, 149, 157, 163, 173, 179, 181, 193, 197, 211, 227, 229, 241, 251, 269, 277, 283, 293, 307, 313, 317, 331, 347, 349, 373, 379, 389, 397, 401, 409, 419, 421, 433, 443

Offset

1,1

Comments

Complement of A049584 relative to A000040.

Links

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

Mathematica

ok[p_] := Reduce[Mod[x^52 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[100]], ok] (* Vincenzo Librandi, Sep 21 2012 *)

Prog

(Magma) [p: p in PrimesUpTo(500) | not exists{x: x in ResidueClassRing(p) | x^52 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, 52), print1(p, ", ")));
/* Joerg Arndt, Sep 21 2012 */

Crossrefs

Cf. A000040, A049584.

Sequence in context: A059634 A059315 A045403 * A014662 A059349 A045316

Adjacent sequences: A059638 A059639 A059640 * A059642 A059643 A059644

Keyword

nonn,easy

Author

Klaus Brockhaus, Feb 02 2001

Status

approved