# MultiplicativeOrder understanding

According to specification, this should find the smallest integer $m$ such that $10^m \, mod \, 16 = 0$, or return unevaluated if there is no such integer.

MultiplicativeOrder[10, 16, {0}]

MultiplicativeOrder[10, 16, {0}]

But such integer does exist, for example four:

Divisible[10^4, 16]

True

What am I doing wrong?

• The equality $k^m = 0 \mod n$ is well defined, but the integer $0$ does not belong to a multiplicative group. I think this is the reason why MultiplicativeOrder remains unevaluated in this case. – user31159 Oct 25 '16 at 12:41
• @xavier Can I replace 0 with 1 for example (default remainder), and transform the arguments somehow so the initial equality still holds? – BoLe Oct 25 '16 at 13:00
• @BoLe MultiplicativeOrder[x, 16] should evaluate for any integer x where GCD[x, 16] == 1, i.e. x must be an odd integer. – Chip Hurst Oct 25 '16 at 13:45