The <Plünnecke-Ruzsa inequality> states that, for all <nonnegative integers> $m,n$,
$$
\boxed{|mA-nA|\leq K^{m+n}|A|.}
$$
Here $mA$ is the <iterated sumset> of $m$ copies of $A$, with $0A=\{0\}$. In particular, $|mA|\leq K^m|A|$.

Solution

Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 149 / 1 / a / Solution

 Solution (source code)