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Claim. A sequence $A$ of positive integers is $r$-Ramsey complete if, however it is split into $r$ classes, every sufficiently large integer is a sum of distinct terms from one class. Conlon, Fox and Pham prove (Theorem 1.2, p. 4) that for every degree $k$ there is a constant $C(k)$ such that, for every polynomial $P$ of degree $k$ whose sequence $(P(m))_{m\ge1}$ is complete and every $r\ge2$, that sequence contains an $r$-Ramsey complete subsequence $A$ with $|A\cap[n]|\le C(k)r\log^2n$ for all $n$. At $P(x)=x^2$ and $r=2$ this gives a 2-Ramsey complete subsequence of the squares, and a sequence containing a 2-Ramsey complete subsequence is itself 2-Ramsey complete: any 2-coloring of the squares restricts to the subsequence, whose monochromatic sums of distinct terms are monochromatic sums of distinct squares. So the squares are Ramsey 2-complete, which answers Problem 843 in the affirmative. The theorem's hypothesis, that the squares form a complete sequence, is the classical fact that every sufficiently large integer is a sum of distinct squares; the paper's p. 4 states Graham's criterion for a polynomial sequence to be complete, which $x^2$ satisfies. The library card is Conlon, Fox and Pham 2021, whose Bears-on entry for this problem records the specialization.

Burr's unpublished proof. In Erdős 1995, item 11 of Part I (typescript p. 7), Erdős reports that Burr had a proof that the $k$-th powers are Ramsey $r$-complete for every $k$ and $r$; the proof was never published, and the paper's p. 4 says its theorem subsumes that result. With no manuscript, Burr's proof has no claim page of its own; the problem's standing rests on the published argument above.

Acceptance. The site's curator, Thomas Bloom, labels the problem proved and credits the stronger result to Conlon, Fox and Pham in the page's commentary, which is the reviewed evidence. The paper is an arXiv preprint: its arXiv record lists no journal reference and no published version is recorded, so there is no refereed evidence. No formalization is on record; the community database lists the problem as unformalized.

Scope. The claim covers the problem's question for the squares and, by the same theorem, the $k$-th powers for every $k\ge2$ and every number $r$ of colors, the variant the site's commentary mentions. The constant $C(k)$ is not made explicit in the statement.