A finite set A of integers is square-sum-free if there is no subset of A sums up to a square. In 1986, Erdős 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 n1/3+0(1).
CITATION STYLE
Nguyen, H. H., & Hu, V. H. (2010). Squares in sumsets. In Bolyai Society Mathematical Studies (Vol. 21, pp. 491–524). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-14444-8_14
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