On a sumset problem for integers (Q405084)
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scientific article; zbMATH DE number 6340111
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a sumset problem for integers |
scientific article; zbMATH DE number 6340111 |
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On a sumset problem for integers (English)
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4 September 2014
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Summary: 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 \(|A+4\cdot A|\geq5|A|-6 \) for \(|A|\geq5\).
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additive combinatorics
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sumsets
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