Question 89
For every natural number $n \gt 1$, find all subsets $\{r_0, r_1, \dots, r_k\}$ of distinct positive integers such that
$$
n^n + n^{n-1} + \dots + n + 1 \mid n^{r_k} + \dots + n^{r_1} + n^{r_0}
$$
$$
n^n + n^{n-1} + \dots + n + 1 \mid n^{r_k} + \dots + n^{r_1} + n^{r_0}
$$