# Sums of dilates of finite sets of integers

Let $A$ be a subset of integers and let $2\cdot A+k\cdot A= \{2a_1+ka_2 : a_1,a_2\in A\}$. Y. O. Hamidoune and J. Rué proved that if $k$ is an odd prime and if $A$ is a finite set of integers such that $|A|>8k^k$, then $|2\cdot A+k\cdot A|\ge (k+2)|A|-k^2-k+2$. I will show how to extend this result to the case when $k$ is a power of an odd prime.

Zeljka Ljujic