Periodicity and floor functions in 2016!

Algebra Level 5

\[f(n)= \left \lfloor \dfrac{10^{n+2016}-10^{n+1}}{10^{2016}-1} \right \rfloor - 10\left \lfloor \dfrac{10^{n+2015}-10^n}{10^{2016}-1} \right \rfloor\]

The above function is defined on the set of natural numbers. If the function is periodic find its period, otherwise write 0.

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