Claims

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1979_01_01_hindman: Theorems 4.3 (Graham) and 4.4 of Hindman (Trans. Amer. Math. Soc. 1979): every two-coloring of the positive integers has distinct x, y with x, y, x+y and xy in one color, the case of two colors and |A| = 2.

2026_09_23_openai: The OpenAI release's preprint of 23 September 2026 claims the full statement: every finite coloring of the positive integers has m distinct integers with all nonempty subset sums and products in one color.

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