1. For a natural number $n$, it is known that the last digits (units digits) of $n$ and $n^{2008}$ are the same. Must the last digits of $n$ and $n^{3}$ also coincide?
1. By checking through all possibilities, we find that if the last digits of $n$ and $n^{2008}$ coincide, then they are either 0, 1, 5, or 6. This means that they do not change when raised to any power.