3. For which natural numbers $n$ can the fraction $\frac{4}{n}$ 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: $n=27 ; a_{1}=4, a_{2}=8, a_{3}=1$;

$
n=37 ; a_{1}=0, a_{2}=8, a_{3}=2
$