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Preprint ON A SUMSET PROBLEM FOR INTEGERS

By Shan-shan Du, Hui-qin Cao and Zhi-wei Sun

Abstract

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 ·A | ≥ (k +1)|A|−⌈k(k +2)/4⌉ provided |A | ≥ (k −1) 2 k!, where A+k·A = {a+kb: a,b ∈ A}. We also establish the inequality |A+4·A | ≥ 5|A|−6 for |A | ≥ 5. 1

Topics: A1 +···+Ak | ≥ |A1|+···+|Ak|−k +1
Year: 1011
OAI identifier: oai:CiteSeerX.psu:10.1.1.186.9705
Provided by: CiteSeerX
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