Question 100
For all pairs of $(m, n)$ positive integers that have the same number $k$ of divisors we define the operation $\circ$. Write all their divisors in an ascending order: $1 = m_1 \lt \dots \lt m_k = m$, $1 = n_1 \lt \dots \lt n_k = n$ and set
$$
m \circ n = m_1 \cdot n_1 + \dots + m_k \cdot n_k.
$$
Find all pairs of numbers $(m, n)$, $m \ge n$, such that $m \circ n = 497$.
$$
m \circ n = m_1 \cdot n_1 + \dots + m_k \cdot n_k.
$$
Find all pairs of numbers $(m, n)$, $m \ge n$, such that $m \circ n = 497$.