Statement

Tommaso is tired of the plain, empty walls at his university, so he decides to decorate them with photos and pictures. He has already chosen the perfect photo to start with, but now he faces a challenging task: finding the right frame. Tommaso has a few specific requirements for the frame: (1) It must be rectangular in shape. (2) Its width and height must be integers. (3) Its area must be exactly A. (4) It must be at least as large as his photo, which has dimensions N × M (i.e., the frame's width must be at least N and its height must be at least M). Tommaso is eager to make a quick decision and avoid unsolicited opinions from art students. However, there are so many possible frames that he can't count them all on his own. Can you help him determine how many frames meet his requirements?