CMO 2014 Problem 2

For the integer $n>1$ , define $D(n)=\{ a-b\mid ab=n, a>b>0, a,b\in\mathbb{N} \}$ . Prove that for any integer $k>1$ , there exists pairwise distinct positive integers $n_1,n_2,\ldots,n_k$ such that $n_1,\ldots,n_k>1$ and $|D(n_1)\cap D(n_2)\cap\cdots\cap D(n_k)|\geq 2$ .