KMO 2018 Problem 6

Let $n \ge 3$ be a positive integer. For every set $S$ with $n$ distinct positive integers, prove that there exists a bijection $f: \{1,2, \cdots n\} \rightarrow S$ which satisfies the following condition.

For all $1 \le i < j < k \le n$ , $f(j)^2 \neq f(i) \cdot f(k)$ .