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Standard and easy combo

Source: PErA 2024/1

March 4, 2024
combinatorics

Problem Statement

Let nn be a positive integer, and let [n]={1,2,…,n}[n]=\{1,2,\dots,n\}. Find the maximum posible cardinality of a subset SS of [n][n] with the property that there aren't any distinct a,b,c∈Sa,b,c\in S such that a+b=ca+b=c.
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