Question 24
Let $n$ be a positive integer greater than $1$. The teacher writes $n+1$ positive integers on the blackboard, whereby the last of them, let it be $c$, is not divisible by $n$. Can Mary always denote the first $n$ integers written by the teacher by $a_1, \dots, a_n$ in such an order that the product $(a_1 - a_2) \cdot (a_2 - a_3) \cdot \dots \cdot (a_{n-1} - a_n) \cdot (a_n - a_1)$ were congruent to either $0$ or $c$ modulo $n$?