The multiplicative suborder function assigns to an integer modulo an integer the least positive
integerexponent such that (mod ), or zero if no such exists. Such an exponent exists
iff. For and 1, the suborder is defined to be 0 by convention.
This function is denoted and can be implemented in the Wolfram
Language as:
Martin, O.; Odlyzko, A. M.; and Wolfram, S. "Algebraic Properties of Cellular Automata." Comm. Math. Phys.93, 219-258,
1984. https://doi.org/10.1007/BF01223745.Sloane,
N. J. A. Sequences A103489 and A103491 in "The On-Line Encyclopedia of Integer
Sequences."
modulo an integer 
the least positive
integer exponent 
such that 
(mod 
), or zero if no such 
exists. Such an exponent exists
iff 
. For 
and 1, the suborder is defined to be 0 by convention.
and can be implemented in the Wolfram
Language as:
for small values of 
and 
.
for 
, 1, ...