From dasimov@earthlink.net 1) Better here would be all rows & columns and broken diagonals (i.e., diagonals on the torus) multiply to the same product.
From Christian Boyer I do not know if it is possible, but (...) (...) Another interesting example, magic product 14400: 1 6 40 60 20 120 2 3 24 4 15 10 30 5 12 8 Exchange columns 1 and 2, or columns 3 and 4, or idem for rows: the square remains magic!!! Because each diagonal of the four inside 2x2 squares have always the same magic product 120.
YES, POSSIBLE! Slightly moving numbers in my above 4x4 example, here is a nice pandiagonal multiplicative square: 1 40 6 60 24 15 4 10 20 2 120 3 30 12 5 8 Dan, all is OK: "all rows & columns and broken diagonals (i.e., diagonals on the torus) multiply to the same product" = 14,400 here. Should be the smallest possible product allowing that property! Christian.