Bonjour, As said yesterday, 302400 is the smallest possible product for 5x5 multiplicative squares. And 332640 is another new possible product smaller than our previous example with 362880. Here is one of the numerous possible examples with 302400: 12 35 1 40 18 36 2 24 7 25 14 45 15 4 8 5 16 42 30 3 10 6 20 9 28 coming from the family: aab cd 1 aaac abb aabb a aaab d cc ad bbc bc aa aaa c aaaa abd abc b ac ab aac bb aad magic product a^6 * b^3 * c^2 * d (example with a=2, b=3, c=5, d=7 for 302400, but of course the same family can be used for 423360, 475200, ...) Other numerous families are possible with the same magic product a^6 * b^3 * c^2 * d. Some words on the method used for nxn multiplicative squares. For each "good" P (means with several little factors), the program computes all the magic series of n distinct integers having the product P. For example with n=5: P=302400 has 3527 series, 332640 has 3661 series, 362880 has 3734 series. Then it analyzes combinations of n series looking if it is possible to get n series using n² distinct integers. If n series are found, they are the n rows: arrange them trying to get n columns and 2 diagonals. No great secret in the method... A specific page on multiplicative squares will be added in the next update of www.multimagie.com/indexengl.htm, planned beginning of October. Christian. ------------------------------------------ The 10 smallest magic products for 5x5 are: Prod. = 2^ * 3^ * 5^ * 7^ * 11^ *13^ 302400 6 3 2 1 0 0 << The SMALLEST 332640 5 3 1 1 1 0 362880 7 4 1 1 0 0 << Previously known 393120 5 3 1 1 0 1 << id 332640 403200 8 2 2 1 0 0 415800 3 3 2 1 1 0 423360 6 3 1 2 0 0 << id 302400 443520 7 2 1 1 1 0 475200 6 3 2 0 1 0 << id 302400 491400 3 3 2 1 0 1 << id 415800 ------------------------------------------