46. Given that $\overline{a b}$ is a two-digit number, and $\overline{a b c d e}$ is a five-digit number. If $(\overline{a b})^{3}=\overline{a b c d e}$, find $\overline{a b c d e}$.
Solve $(\overline{a b})^{3}=\overline{a b c d e}=1000 \cdot \overline{a b}+\overline{c d e}$.
We have $\left[(\overline{a b})^{2}-1000\right] \cdot \overline{a b}=\overline{c d e}$.
Thus, $(\overline{a b})^{2}>1000$, which means $\overline{a b}>\sqrt{1000}>31$.
Therefore, $\bar{a} \bar{v} \geqslant 32$.
Also, $(\overline{a b})^{2}-1000=\frac{\overline{c d e}}{\overline{a b}} \leqslant \frac{999}{32}<32$,
Therefore, $(\overline{a b})^{2}<1032$, which means $\overline{a b}<\sqrt{1032}<33$.
Hence, $\overline{a b}=32,32^{3}=32768$.
Therefore, the required $\overline{a b c d e}$ is 32768.