A049577 Primes p such that x^45 = 2 has a solution mod p.

2, 3, 5, 17, 23, 29, 43, 47, 53, 59, 83, 89, 107, 113, 127, 137, 149, 157, 167, 173, 179, 197, 223, 227, 229, 233, 239, 251, 257, 263, 269, 277, 283, 293, 317, 347, 353, 359, 383, 389, 397, 419, 431, 439, 443, 449, 457, 467, 479, 499, 503, 509, 557, 563, 569, 587, 593, 599, 617, 641, 643, 647

Offset

1,1

Comments

Complement of A059637 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^45 - 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[120]], ok] (* Vincenzo Librandi, Sep 14 2012 *)

Prog

(Magma) [p: p in PrimesUpTo(600) | exists(t){x : x in ResidueClassRing(p) | x^45 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, 45), print1(p, ", ")));
/* Joerg Arndt, Sep 21 2012 */

Crossrefs

Cf. A000040, A059637.

Sequence in context: A032733 A111632 A049547 * A353153 A121558 A240679

Adjacent sequences: A049574 A049575 A049576 * A049578 A049579 A049580

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved