For certain pairs (m, n) of positive integers with m \geq n there are exactly 50 distinct positive integers k such that |\log m-\log k|<\log n. Find the sum of all possible values of the product m n.
For certain pairs (m, n) of positive integers with m \geq n there are exactly 50 distinct positive integers k such that |\log m-\log k|<\log n. Find the sum of all possible values of the product m n.