Show that: 1) If $2n-1$ is a prime number, then for any $n$ pairwise distinct positive integers $a_1, a_2, \ldots , a_n$, there exists $i, j \in \{1, 2, \ldots , n\}$ such that \[\frac{a_i+a_j}{(a_i,a_j)} \geq 2n-1\] 2) If $2n-1$ is a composite number, then there exists $n$ pairwise distinct positive integers $a_1, a_2, \ldots , a_n$, such that for any $i, j \in \{1, 2, \ldots , n\}$ we have \[\frac{a_i+a_j}{(a_i,a_j)} < 2n-1\] Here $(x,y)$ denotes the greatest common divisor of $x,y$.