Question 19
Find all positive integers $m$ such that there exists an infinite set $A$ of positive integers satisfying: for any $m$ distinct elements $a_1, a_2, \dots, a_m$ in $A$, both $a_1+a_2+\dots+a_m$ and $a_1a_2\cdots a_m$ are square-free.
*Note: A positive integer $n$ is called square-free if it is not divisible by the square of any prime number.*
*Note: A positive integer $n$ is called square-free if it is not divisible by the square of any prime number.*