[math-fun] add-mult magic squares

I'm curious about small addition-multiplication squares. Assume we ditch the integer requirement, and allow real or complex numbers - presumably algebraic. We keep the requirement that the elements are distinct. If we drop the diagonals, then simple counting of constraints suggests there should be a 4x4 with a couple of degrees of freedom remaining; and there should be 5x5s for which the diagonals work. This seems like a good problem for multiple approaches: multivariate hill climbing; or some heavy-duty algebra. Rich