Claims

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2003_03_01_croot: Croot's theorem that every r-coloring of the integers from 2 to b^r has a monochromatic set with reciprocal sum one, answering the finite-coloring question for the integers by restriction to that interval.

2021_12_07_bloom: Bloom's theorem that every set of positive upper density contains a finite set with reciprocal sum one; one color class of any finite coloring of the integers has positive upper density, so the coloring question follows.

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