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

1,5

Links

Table of n, a(n) for n=1..84.

Mathematica

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

Prog

(PARI) a(n) = {for (i = 1, eulerphi(n), if ((9^i % n) == 1, return(i)); ); return (0); } \\Michel Marcus, Jul 31 2013
(Magma) [0] cat [Modorder(9, n): n in [2..100]]; // Vincenzo Librandi, Apr 01 2014

Crossrefs

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

Sequence in context: A269517 A190440 A054372 * A177443 A176919 A220645

Adjacent sequences: A070676 A070677 A070678 * A070680 A070681 A070682

Keyword

nonn

Author

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

Status

approved