Question 66
Let $n \geqslant 2$ be an integer. Anna has written on the board $n$ pairwise distinct integers $a_{1}, a_{2}, \ldots, a_{n}$. She then notices that, whichever way one selects $n-1$ of these integers, their sum is divisible by $n$.
Prove that the sum of all $n$ integers is divisible by $n$.
Prove that the sum of all $n$ integers is divisible by $n$.