Question 8
Let $a_1 \lt a_2 \lt \dots$ be the positive divisors of a positive integer $a$ and let $b_1 \lt b_2 \lt \dots$ be the positive divisors of a positive integer $b$. Find all $a, b$ such that
$$
\begin{cases} a_{10} + b_{10} = a \\ a_{11} + b_{11} = b \end{cases}
$$
$$
\begin{cases} a_{10} + b_{10} = a \\ a_{11} + b_{11} = b \end{cases}
$$