| $\left[\begin{array}{l}{\left[\begin{array}{l}\text { Decimal numeral system }\end{array}\right]} \\ {[\text { Examples and counterexamples. Constructions }]}\end{array}\right.$ |
| :---: | :---: |

Does there exist a digit $a$ such that $\overline{\operatorname{aaa(a-1)}}=(a-1)^{a-2}$.
When $a=7$, we get the correct equality $7776=6^{5}$.

## Answer

It exists.