MathNet 2017-part-03 — 176 problems (EN–VI) Question 134

Let $x_{1}, x_{2}, x_{3}, \ldots$ be a sequence of positive integers such that, for all positive integers $m, n$, we have $x_{m n} \neq x_{m(n+1)}$. Prove that there exists a positive integer $i$ such that $x_{i} \geq 2017$.