Question 42
The treasurer of Math republic chose a number $\alpha \gt 2$ and issued coins with values of 1 rouble and of $\alpha^k$ roubles for all positive integer $k$. It turns out that all the values of coins (except for 1) are irrational. May it happen that for any positive integer $n$, one may take several coins whose values sum up to $n$ roubles so that the coins of each value are taken at most six times? (I. Bogdanov, S. Berlov)