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Romania Junior TST 2022 Day 1 P5

Source: Romania JBMO TST 2022

April 20, 2022
combinatoricsRomanian TST

Problem Statement

We call a set A⊂RA\subset \mathbb{R} free of arithmetic progressions if for all distinct a,b,c∈Aa,b,c\in A we have a+b≠2c.a+b\neq 2c. Prove that the set {0,1,2,…38−1}\{0,1,2,\ldots 3^8-1\} has a subset AA which is free of arithmetic progressions and has at least 256256 elements.
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