On the sum of dilations of a set
Volume 164 / 2014
Acta Arithmetica 164 (2014), 153-162
MSC: 11B13, 05B10, 11B30.
DOI: 10.4064/aa164-2-5
Abstract
We show that for any relatively prime integers $1\leq p< q$ and for any finite $A \subset \mathbb {Z}$ one has $$|p \cdot A + q \cdot A | \geq (p + q) |A| - (pq)^{(p+q-3)(p+q) + 1}.$$
