National Olympiad Final Round

For example, numbers $x=2016\cdot 2015-2018$ and $y=2018$ meet the conditions. As $2016\cdot 2015>4\cdot 1009=2\cdot 2018$ implies $x>y$, they are distinct. The sum $2016\cdot 2015$ is divisible by $2016$ and the product is obviously divisible by $2018$. Furthermore, $x-y=2016\cdot 2015-2\cdot 2018=(2017-1)(2017-2)-2\cdot (2017+1)=2017^2-3\cdot 2017+2-2\cdot 2017-2=2017\cdot 2012$, whence the difference of these numbers is divisible by $2017$.