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

{title2=$mA$}

For a <nonnegative integer> $m$, the iterated sumset $mA$ is the sum of $m$ copies of $A$, with $0A=\{0\}$. Repetitions are allowed, so its elements are sums $a_1+\cdots+a_m$ with each $a_i\in A$.

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 Incoming links: Iterated sumset