Given an integer $n > 1$, prove that there exist distinct positive integers $a, b, c$ and $d$ such that $a + b = c + d$ and $\frac{a}{b}=\frac{nc}{d}$.
Source: Tournament of towns spring 2011
Tags: number theory
Given an integer $n > 1$, prove that there exist distinct positive integers $a, b, c$ and $d$ such that $a + b = c + d$ and $\frac{a}{b}=\frac{nc}{d}$.