My program (WM 10.02): FunctionPeriod[PowerModList[n, 1/4, 9], n, Integers]
PowerModList::arg1 : "The first argument [NoBreak]\!(n)[NoBreak] \ of PowerModList is not an integer. (many same words) 0
When i try
FunctionPeriod[Mod[n, 9], n, Integers]
it works, answer: 9
Maybe, it's a bug (or it's only on my comp)?
You are right, i think.
maybe, in the next version WM we'll see more options of FunctionPeriod...
It seems that PowerModList is only designed for numeric n. Perhaps because it is a list-valued function, not a numeric-valued function. I may be wrong, though.