Claims

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1989_03_01_bosznay: Bosznay's 1989 theorem that the largest non-averaging subset of the first N integers exceeds c N^{1/4} for large N, by the set i q^3 + i(i+1)/2 for i = 1, ..., q-1; the lower half of the answer, refereed and site-credited.

2024_10_18_pham_zakharov: Pham and Zakharov's theorem that every non-averaging subset of the first N integers has at most N^{1/4+o(1)} elements, which with Bosznay's bound gives F(N)=N^{1/4+o(1)}; in Geom. Funct. Anal. 2025, adopted by the site.

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