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arXiv · 1311.0422

On the Sum of Dilations of a Set

Antal Balog·George Shakan
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Abstract

We show that for any relatively prime integers $1\leq p<q$ and for any finite $A \subset \mathbb{Z}$ one has $$|p \cdot A + q \cdot A | \geq (p + q) |A| - (pq)^{(p+q-3)(p+q) + 1}.$$

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Antal Balog, George Shakan. 2013-11-19. On the Sum of Dilations of a Set. https://arxiv.org/abs/1311.0422

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