I was shown a 4x4 matrix whose entries are distinct positive integers below 32, whose row sums are the same (say S), and whose column products are the same (P).

I believe that there are numerous solutions fitting the above definition, and challenge the solvers to find as many as possible - the values of S and P are up to you.

Rem : It is possible to find a solution or two without a computer, but listing all possible solutions is IMHO a hard nut even for a software-based approach.