Claims

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1999_04_01_erdos_lev_rauzy_sandor_sarkozy: Erdős, Lev, Rauzy, Sándor and Sárközy's refereed bounds (Discrete Math. 1999) on the largest non-dividing subset of the first N integers: F(N) < 3 N^{1/2} + 1 for all N, and F(N) >> N^{1/5} deduced from Straus and Bosznay.

2024_10_18_pham_zakharov: Pham and Zakharov's refereed bound (Geom. Funct. Anal. 2025) of N to the 1/4 + o(1) for non-averaging sets, which non-dividing sets are, so the displayed question, whether F(N) exceeds N to the 1/2 - o(1), is answered no.

2026_07_24_xeff: A full proof claim of 24 July 2026 by Theofil Xeff, made with GPT 5.6 Sol and Fable 5: F(N) equals N to the 1/5 + o(1), by a normalization of the Pham-Zakharov density-increment argument; unexamined by the site.

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