Christian writes: << Dan, you are right, there is a great relationship between additive and multiplicative squares (and cubes), but not always a direct relationship.
I may have been less than clear. Considering only conditions on rows & columns, all I was saying is that, suppose p_k is the largest prime divisor of any entry in a MuMaSq: Then if each entry p_1^e_1 * . . . * p_k^e_k (all e_j >= 0) is replaced by its tuple of exponents (e_1,...,e_k), the result is an AdMaSq -- not of mere integers, but of k-tuples of integers. Or if you prefer, k ordinary magic squares (possibly with repeated entries), one for each j in {1,...,k}, each created by replacing each entry in the MuMaSq by its jth exponent, e_j. And conversely, though extra care must be taken to assure that all final entries be distinct. --Dan