Problem

Source: Poland 73-3-2

Tags: number theory



Let $m,n\ge 2$ be given integers. Prove that there exist positive integers $a_1<a_2<\ldots<a_m$ so that for any $1\le i<j\le m$ the number $\frac{a_j}{a_j-a_i}$ is an integer divisible by $n$.