So, a simple perfect squaring of a rectangle is a tiling of that rectangle by squares whose side lengths are all distinct integers. Additionally, not subset of the squares must form a smaller rectangle. My question is if there is a simple perfect squaring of a 1366 by 768 rectangle?
We could try reducing it to a simpler problem by splitting the rectangle into a square and a smaller rectangle, but then we need to ensure that the side lengths are different, and that the their combination is simple. So we basically back to where we started.
P.S. If you are wondering why 1366 by 768, that's the dimension of my monitor, which I am trying to artistically square (hence the art tag).