Problem 843

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?

Source: erdosproblems.com/843

Number theory

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An accepted solution exists. The statement is true.

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.

Problem 843

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