
TL;DR
This paper investigates the maximum size of square-sum-free subsets within initial segments of natural numbers, establishing that the largest such set grows roughly as n^{1/3} as n increases.
Contribution
The paper provides an asymptotic estimate for the maximum size of square-sum-free subsets, resolving a problem posed by Erdős in 1986.
Findings
Maximum size of square-sum-free sets is of order n^{1/3+o(1)}
Established asymptotic growth rate for these sets
Answer to Erdős's problem from 1986
Abstract
A finite set of integers is square-sum-free if there is no subset of 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 . Answering this question, we show that this maximum cardinality is of order .
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Taxonomy
TopicsGraph Labeling and Dimension Problems · Limits and Structures in Graph Theory · graph theory and CDMA systems
