A059636 Primes p such that x^44 = 2 has no solution mod p.

3, 5, 11, 13, 17, 19, 23, 29, 37, 41, 43, 53, 59, 61, 67, 83, 89, 97, 101, 107, 109, 131, 137, 139, 149, 157, 163, 173, 179, 181, 193, 197, 199, 211, 227, 229, 241, 251, 269, 277, 283, 293, 307, 313, 317, 331, 347, 349, 353, 373, 379, 389, 397, 401, 409, 419

Offset

1,1

Comments

Complement of A049576 relative to A000040.

Links

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

Mathematica

ok[p_] := Reduce[Mod[x^44 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[90]], ok] (* Vincenzo Librandi, Sep 21 2012 *)

Prog

(Magma) [p: p in PrimesUpTo(500) | not exists{x: x in ResidueClassRing(p) | x^44 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, 44), print1(p, ", ")));
/* Joerg Arndt, Sep 21 2012 */

Crossrefs

Cf. A000040, A049576.

Sequence in context: A065396 A020620 A136056 * A087894 A245048 A338018

Adjacent sequences: A059633 A059634 A059635 * A059637 A059638 A059639

Keyword

nonn,easy

Author

Klaus Brockhaus, Feb 02 2001

Status

approved