TOPICS

# Suborder Function

The multiplicative suborder of a number (mod ) is the least exponent such that (mod ), or zero if no such exists. An always exists if and .

This function is denoted and can be implemented in the Wolfram Language as:

```  Suborder[a_,n_] := If[n>1&& GCD[a,n] == 1,
Min[MultiplicativeOrder[a, n, {-1, 1}]],
0
]```

The following table summarizes for small values of and .

 OEIS for , 1, ... 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, ...

Multiplicative Order

This entry contributed by Tony Noe

## Explore with Wolfram|Alpha

More things to try:

## 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--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/SuborderFunction.html