Problem

Source: Moldova TST 2018

Tags: number theory, number of divisors



The positive integers $a $ and $b $ satisfy the sistem $\begin {cases} a_{10} +b_{10} = a \\a_{11}+b_{11 }=b \end {cases} $ where $ a_1 <a_2 <\dots $ and $ b_1 <b_2 <\dots $ are the positive divisors of $a $ and $b$ . Find $a$ and $b $ .