矩形整数边问题 from WXC

sean9991

by induction.  we can shrink the rectangle in the following way.  consider the top left corner small rectangle.  if it's vertical side is integer length, we cut the large rectangle along the bottom of the small rectangle.  therefore, we reduce the vertical side of the large rectangle by an integer length.  if not, then the horizontal side is integer length, we cut the large rectangle along the right side of the small rectangle.  we reduce the horizontal side of the large rectangle by an integer length.  Note the condition still holds with the shrinked rectangle and the smaller rectangles (at least one of their sides are integer lengths).  Eventually, the larger rectangle will have either vertical / horizontal side equals 1. www.ddhw.com