On the Sum of Dilations of a Set
classification
🧮 math.NT
keywords
cdotdilationsfiniteintegersmathbbprimerelativelysubset
read the original 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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