Question 115
Given $n \ge 3$ Pairwise coprime positive integers. It is known that while dividing the product of any $n-1$ of them by the remaining number $r$ (The Remainder $r$ Is the same for all $(n-1)$-tuples). prove that $r \le n-2$. Are given $n \ge 3$ Pair of mutually prime numbers. It is known that when dividing the work of any $n-1$ From them, the remaining number is the same residue $r$. Prove that $r \le n-2$. (V. Senders)