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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 aninteger side length of at least 2. In particular, we prove that tiling isalways 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 isdetermined computationally by an exhaustive search.

When Can You Tile an Integer Rectangle with Integer Squares?