Monochromatic finite sums and products in the positive integers
We prove Hindman's finite sums and products conjecture: for every finite coloring of the positive integers and every positive integer k, there is a k-element set whose nonempty subset sums and nonempty subset products all have the same color.
Cite
@misc{OAI:Monochromatic-finite-sums-and-products-in-the-positive-integers-September-23-2026,
author = {{OpenAI}},
title = {{Monochromatic finite sums and products in the positive integers}},
howpublished = {OpenAI Math Release preprint
\href{https://github.com/openai/math/blob/main/preprints/Monochromatic-finite-sums-and-products-in-the-positive-integers-September-23-2026/paper.pdf}{OAI:Monochromatic-finite-sums-and-products-in-the-positive-integers-September-23-2026}},
year = {2026}
}