Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dense sumsets of Sidon sequences   Let $k \ge 2$ be an integer. We say a set $A$ of positive integers is an
asymptotic basis of order $k$ if every large enough positive integer can be
represented as the sum of $k$ terms from $A$. A set of positive integers $A$ is
called Sidon set if all the two terms sums formed by the elements of $A$ are
different. Many years ago P. Erd\H{o}s, A. S\'ark\"ozy and V. T. S\'os asked
whether there exists a Sidon set which is asymptotic basis of order $3$. In
this paper we prove the existence of a Sidon set $A$ with positive lower
density of the three fold sumset $A + A + A$ by using probabilistic methods.

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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: cs
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The categories of this paper are: hep-th
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The categories of this paper are: econ
5
The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: hep-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin