Question 129
a) A number $m$ is called **mirror-symmetry** if it is possible to divide the reverse decimal expansion of $m$ into some blocks such that the multiply of these blocks is equal to $m$. For instance, numbers $6$, $543$ and $21$ are such blocks for number $123456$; if the multiply of these $3$ numbers was equal to $123456$, we would call it a **mirror-symmetry** number. Find all **mirror-symmetry** numbers with decimal digits of $\{1, 2, 3\}$.
b) A number $m$ is called **good** if it is possible to divide $m$ itself into some blocks with multiply of $m/7$. Prove that there are infinitely many **good** numbers.
b) A number $m$ is called **good** if it is possible to divide $m$ itself into some blocks with multiply of $m/7$. Prove that there are infinitely many **good** numbers.