Problem 843

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claims/: The 1 claim page of Problem 843, one per claimant's result; the problem's standing derives from them.

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Statement. Are the squares Ramsey $2$-complete?

That is, is it true that, in any 2-colouring of the square numbers, every sufficiently large $n\in \mathbb{N}$ can be written as a monochromatic sum of distinct squares?

Status. Proved.

Source. erdosproblems.com/843, accessed 2026-09-04. Cite as: T. F. Bloom, Erdős Problem #843, https://www.erdosproblems.com/843.

References.

• [BuEr85] Burr, S. A. and Erdős, P., A Ramsey-type property in additive number theory. Glasgow Math. J. (1985), 5-10.
• [CFP21] Conlon, D. and Fox, J. and Pham, H. T., Subset sums, completeness and colorings. arXiv:2104.14766 (2021).
• [Er92b] Erdős, Paul, Some of my favourite problems in various branches of combinatorics. Matematiche (Catania) (1992), 231-240.
• [Er95] Erdős, Paul, Some of my favourite problems in number theory, combinatorics, and geometry. Resenhas (1995), 165-186.

Formalization. None recorded.

Progress

Not yet compiled.

Known Results

Not yet compiled.

Linked library material

These entries are derived from explicit links on library pages. They are navigation only and do not by themselves record mathematical progress.

• conlon_2021_subset_sums_completeness_colorings
• erdos_1995_my_favourite_problems_number_theory_combinatorics