Claims

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2003_03_01_croot: Croot's 2003 coloring paper is credited, by the site and by Liu and Sawhney, with showing that A(N) is below cN for some constant c less than one and all large N, refuting the expected A(N) = (1 + o(1))N.

2024_04_10_liu_sawhney: Liu and Sawhney prove that every subset of one through N of size at least (1 - 1/e + epsilon)N has a subset with reciprocal sum one, which with the trivial top-segment example gives A(N) = (1 - 1/e + o(1))N.

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