The problem is described as follows. Let $c_1=p_1q_1+r$, $c_2=p_2q_2+r$, $\cdots$, $c_n=p_nq_n+r$, where $p_i$'s, $q_i$'s, $r$ are all large positive integers, and $p_i$'s and $q_i$'s are randomly chosen. Notice that $p_i$'s and $q_i$'s are different while $r$ is the same. Now one knows $c_1,\cdots,c_n$, and he knows the above structure of $c_1,\cdots,c_n$, but he does not know $p_i$'s or $q_i$'s. He aims to extract the value of $r$ from $c_1,\cdots,c_n$. Is this problem hard (either proven to be hard, or no polynomial solving algorithm found yet)? Does this problem have a name?