$\displaystyle n=\overline{a_1a_2\dots a_n}$ and define $\displaystyle f(n)=\overline{a_na_{n-1}\dots a_1}$. Find all the positive $\displaystyle k$ integers to which $\displaystyle k|f(n)$ if $\displaystyle k|n$ (in other words: for any multiple of $\displaystyle k$ (which is $\displaystyle n$) $\displaystyle k|f(n)$).