Question 61
Let $m$ be any natural number. Depending on $m$, determine the smallest natural number $k$ for which: If $\{m, m+1, \ldots, k\}=A \cup B$ is an arbitrary decomposition into two sets $A$ and $B$, then $A$ or $B$ contains three elements $a, b, c$ (which are not necessarily different must) with $a^{b}=c$.