Question 79
The natural number $n \gt 1$ is "good" if for every natural numbers $b_1, b_2, \dots, b_{n-1}$ such that $1 \le b_1, b_2, \dots, b_{n-1} \le n-1$ there exists $I \subseteq \{1, 2, \dots, n-1\}$ such that $\sum_{k \in I} b_k \equiv i \pmod n$, for every $i \in \{0, 1, \dots, n-1\}$ (the empty sum is equal to zero). Find all the "good" numbers.