  This paper characterizes when an $m \times n$ rectangle, where $m$ and $n$
are integers, can be tiled (exactly packed) by squares where each has an
integer side length of at least 2. In particular, we prove that tiling is
always possible when both $m$ and $n$ are sufficiently large (at least 10).
When one dimension $m$ is small, the behavior is eventually periodic in $n$
with period 1, 2, or 3. When both dimensions $m,n$ are small, the behavior is
determined computationally by an exhaustive search.
