# Filling a rectangle with squares of integer side length

How many ways are there to fill a $m\times n$ rectangles with squares that have integer side lengths?

Both $m$ and $n$ are integers.

• Dissections of a rectangle into squares can be very complicated, it is hard to even to obtain a general description for them, not saying even to count them. I think there is only hope to obtain some bounds. – Alex Ravsky Jun 18 '15 at 4:48
• Also you may try to ask this question to Erich Friedman (efriedma@stetson.edu). – Alex Ravsky Jun 18 '15 at 4:56