The multiplicative suborder of a number
This function is denoted Wolfram
Language as:
Suborder[a_,n_] := If[n>1&& GCD[a,n] == 1,
Min[MultiplicativeOrder[a, n, {-1, 1}]],
0
]
The following table summarizes
OEIS 2 0, 0, 0, 1, 0, 2, 0, 3, 0, 3, 0, 5, 0, 6, 0, ... 3 A103489 0, 0, 1, 0, 1, 2, 0, 3, 2, 0, 2, 5, 0, 3, 3, ... 4 0, 0, 0, 1, 0, 1, 0, 3, 0,
3, 0, 5, 0, 3, 0, ... 5 A103491 0, 0, 1, 1, 1, 0,
1, 3, 2, 3, 0, 5, 2, 2, 3, ...
See also Multiplicative Order
This entry contributed by Tony Noe
Explore with Wolfram|Alpha
References Sloane, N. J. A. Sequences A103489 and A103491 in "The On-Line Encyclopedia
of Integer Sequences." Wolfram, S.; Martin, O.; and Odlyzko, A. M.
"Algebraic Properties of Cellular Automata." Comm. Math. Phys. 93 ,
219-258, 1984. Referenced on Wolfram|Alpha Suborder Function
Cite this as:
Noe, Tony . "Suborder Function." From MathWorld Eric
W. Weisstein . https://mathworld.wolfram.com/SuborderFunction.html
Subject classifications
(mod 
) is the least exponent 
such that 
(mod 
), or zero if no such 
exists. An 
always exists if 
and 
.
and can be implemented in the Wolfram
Language as:
for small values of 
and 
.
for 
, 1, ...