3. For which natural numbers $n$ can the fraction $\frac{5}{n}$ be represented as a periodic decimal fraction of the form $0.1\left(a_{1} a_{2} a_{3}\right)$ with a period containing at least two different digits?
Answer: $n=27 ; a_{1}=8, a_{2}=5, a_{3}=1$;

$$
n=37 ; a_{1}=3, a_{2}=5, a_{3}=1
$$