Hindman's monochromatic sum-product quadruple question

Let a finite partition of N\mathbb{N} be given. Hindman's question. There exist x,yNx,y\in\mathbb{N} such that

{x,y,x+y,xy}\{x,y,x+y,xy\}

is monochromatic. This asks whether every finite coloring of the positive integers contains a monochromatic configuration simultaneously involving two numbers, their sum, and their product.

Sources & referencesView supporting material

Primary source

Conner Griffin, “Infinite Sum-Product Configurations in Parallel”, arXiv:2605.24751 (2026).

Additional references

3 papers in this index state this conjecture (2020–2026). The statement above is taken from the most recent of them; the others are arXiv:2507.00515, arXiv:2003.10161.

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