If an m×n rectangle is minimally divisible into k integer-sided squares, it it ever the case that a 2m×2n rectangle can be divided into fewer squares? https://mathoverflow.net/questions/116382/tiling-a-rectangle-with-the-smalle... The (7125×7081) rectangle seems to need 21 squares. The 2(7125×7081) rectangle only needs 20 squares. Pictures at the link. --Ed Pegg Jr