A070679 Smallest m in range 1..phi(n) such that 9^m == 1 mod n, or 0 if no such number exists.

0, 1, 0, 1, 2, 0, 3, 1, 0, 2, 5, 0, 3, 3, 0, 2, 8, 0, 9, 2, 0, 5, 11, 0, 10, 3, 0, 3, 14, 0, 15, 4, 0, 8, 6, 0, 9, 9, 0, 2, 4, 0, 21, 5, 0, 11, 23, 0, 21, 10, 0, 3, 26, 0, 10, 3, 0, 14, 29, 0, 5, 15, 0, 8, 6, 0, 11, 8, 0, 6, 35, 0, 6, 9, 0, 9, 15, 0, 39, 2, 0, 4, 41, 0

Offset: 1

Author

N. J. A. Sloane and Amarnath Murthy, May 08 2002

Keywords

• nonn

Crossrefs

Cf. A070667-A070675, A002326, A070676, A053447, A070677, A070681, A070678, A053451, A070682, A070680, A070683.

Programs

Magma

[0] cat [Modorder(9, n): n in [2..100]]; // Vincenzo Librandi, Apr 01 2014

Mathematica

Table[SelectFirst[Range[EulerPhi[n]],PowerMod[9,#,n]==1&],{n,90}]/. Missing[ "NotFound"] -> 0 (* Harvey P. Dale, Jan 22 2023 *)

PARI

a(n) = {for (i = 1, eulerphi(n), if ((9^i % n) == 1, return(i));); return (0);} \\Michel Marcus, Jul 31 2013