[math-fun] Sum-Product Magic Square

I wrote a brute force program to generate 3x3 magic product squares. The findings lead me to conjecture that these squares, up to rotation and reflection, are of the form ac bbc aabc aabbc abc c bc aac abbc where a, b, c are chosen so as to make all cells distinct. If this is true, then a 3x3 magic square with all cells distinct cannot be at once additively and multiplicatively magic. I imagine the additive 3x3 magic squares have been fully parameterized, I suppose a proof should have been attempted from that tack. -------------------------------- - David Wilson