Dan, I better understand what you meant about the relationship between additive and multiplicative squares. But, as you wrote, "ordinary magic squares possibly with repeated entries", and "extra care must be taken to assure that all final entries be distinct" in multiplicative squares. Using your split, and as remarked by Michael, my 6x6 pandiagonal magic square is coming from two matrixes, one for 2^: 5 0 4 5 0 4 1 6 2 1 6 2 5 0 4 5 0 4 1 6 2 1 6 2 5 0 4 5 0 4 1 6 2 1 6 2 and its transpose for 3^: 5 1 5 1 5 1 0 6 0 6 0 6 4 2 4 2 4 2 5 1 5 1 5 1 0 6 0 6 0 6 4 2 4 2 4 2 Difficult to call them magic squares because they use (a lot of) repeated entries. Of course, it is trivial to construct a multiplicative magic square from any normal additive magic square, replacing each entry n by 2^n. But very difficult to see a general construction method of the best possible multiplicative magic squares: no known direct correspondence between additive squares <-> multiplicative squares with THE smallest possible integers and product. And find these best possible multiplicative squares (or cubes) are the interesting question. Christian.