Squares in sumsets

Details Squares in sumsets Squares in sumsets

2008-11-09

arxiv.org/abs/0811.1311v2

Mathematics

Combinatorics

33 pages

Scientific paper

A finite set $A$ of integers is square-sum-free if there is no subset of $A$
sums up to a square. In 1986, Erd\H os posed the problem of determining the
largest cardinality of a square-sum-free subset of $\{1, ..., n \}$. Answering
this question, we show that this maximum cardinality is of order
$n^{1/3+o(1)}$.

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