Prove or disprove the following statements. a) For every integer $ n \ge 3$, there exist $ n$ pairwise distinct positive integers such that the product of any two of them is divisible by the sum of the remaining $ n - 2$ numbers. b) For some integer $ n \ge 3$, there exist $ n$ pairwise distinct positive integers, such that the sum of any $ n - 2$ of them is divisible by the product of the remaining two numbers.
Problem
Source: Final Round Grade 12 Pro 3
Tags: modular arithmetic, number theory unsolved, number theory