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.

翻译：本文刻画了当$m$和$n$为整数时，一个$m \times n$矩形能否被边长至少为2的整数正方形精确铺满（即完全覆盖）。特别地，我们证明当$m$和$n$均足够大（至少为10）时，铺满总是可行的。当一个维度$m$较小时，该性质在$n$上最终呈现周期为1、2或3的周期性行为。当两个维度$m,n$均较小时，该性质可通过穷举搜索计算确定。