Squares in sumsets

2008/11/09 by Hoi H. Nguyen, Nguyen, Hoi, Van V. Vu +1
Computer Science · Engineering · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory #Number Theory (math.NT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.0811.1311

openalex publication_date 2008/11/09 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

Abstract

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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