MathNet 2022-part-05 — 197 problems (EN–VI) Question 4

Find all pairs of natural numbers $k$ and $n$ for which the fraction $\frac{4^{k-1}}{n}$ has, in decimal notation, the form $0. \bar{n}$, where $\bar{n}$ denotes the period. For example, if $n=720$, then $0. \bar{n}=0.720720720 \ldots$