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arXiv · 1011.5438

On a sumset problem for integers

Shan-Shan Du·Hui-Qin Cao·Zhi-Wei Sun
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Abstract

Let $A$ be a finite set of integers. We show that if $k$ is a prime power or a product of two distinct primes then $$|A+k\cdot A|\geq(k+1)|A|-\lceil k(k+2)/4\rceil$$ provided $|A|\geq (k-1)^{2}k!$, where $A+k\cdot A=\{a+kb:\ a,b\in A\}$. We also establish the inequality $|A+4\cdot A|\geq 5|A|-6 $ for $|A|\geq 5$.

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Shan-Shan Du, Hui-Qin Cao, Zhi-Wei Sun. 2014-02-20. On a sumset problem for integers. https://arxiv.org/abs/1011.5438

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