Sumsets avoiding squarefree integers

Details Sumsets avoiding squarefree integers Sumsets avoiding squarefree integers

2011-05-06

arxiv.org/abs/1105.1305v1

Acta Arith. 143 (2010), no. 1, 51-53, 11P70

Mathematics

Number Theory

Scientific paper

10.4064/aa143-1-3

We describe the structure of a set of integers $A$ of positive density
$\delta$, such that $A+A$ contains no squarefree integer. It turns out that the
behaviour changes abruptly at the values
$\delta_0=1/4-\frac{2}{\pi^2}=0.0473...$ and $\delta_1=1/18$.

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