Is this an $NP$-complete problem: Product-2-Partition
Denote these integers by $x_1\ge x_2\ge\cdots\ge x_n$. We assume these integers are all positive (it is not hard to revise the following algorithm for instances including both positive and negative integers). 

In a valid solution, the greatest element must match the smallest element. Otherwise, say $x_1$ matches $x_i$ where $x_i&gt;x_n$, and $x_n$ matches $x_j$, then $B=x_1x_i&gt;x_1x_n\ge x_jx_n=B$, a contradiction. Hence a valid solution can only be $\{x_1,x_n\},\{x_2,x_{n-1}\},\ldots$ We only need to check whether this partition is valid, i.e. whether $x_1x_n=x_2x_{n-1}=\cdots=B$.