Question 81
Let be given a positive integer $n \geq 3$. Consider integers $a_{1}, a_{2}, \ldots, a_{n} \gt 1$ with the product equals to $A$ such that: for each $k \in \{1,2, \ldots, n\}$ then the remainder when $\frac{A}{a_{k}}$ divided by $a_{k}$ are all equal to $r$. Prove that $r \leq n-2$.