Question 22
Find all nonzero digits $a, b, c$ such that
$$
\frac{\overline{abc} + a + b + c}{ab + bc + ca}
$$
is an integer.
Notation: $\overline{abc}$ denotes the number whose digits are $a, b, c$, in that order.
$$
\frac{\overline{abc} + a + b + c}{ab + bc + ca}
$$
is an integer.
Notation: $\overline{abc}$ denotes the number whose digits are $a, b, c$, in that order.