My program (WM 10.02): FunctionPeriod[PowerModList[n, 1/4, 9], n, Integers]
answer:
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)?