[Submitted on 19 Jan 2013 (v1), last revised 29 Jul 2026 (this version, v3)]

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Abstract:Answering a question of P. Erdos from 1965, we show that for every eps>0 there is a set A of n integers with the following property: every subset A' of A with at least (1/3 + eps)n elements contains three distinct elements x,y,z with x + y = z.

Submission history

From: Ben Green [view email]
[v1] Sat, 19 Jan 2013 17:22:19 UTC (30 KB)
[v2] Mon, 28 Jan 2013 14:24:43 UTC (30 KB)
[v3] Wed, 29 Jul 2026 09:17:08 UTC (30 KB)

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