We show that if A ⊂ {1,.. ., N} contains no nontrivial three-term arith- metic progressions then |A| = O(N/ log1-o(1)N).
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Sanders, T. (2011). On Roth’s theorem on progressions. Annals of Mathematics, 174(1), 619–636. https://doi.org/10.4007/annals.2011.174.1.20
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