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Claim. The set $\{n^2+1/n:n\in\mathbb{N}\}$ is strongly complete: for every finite set $B$, every sufficiently large integer is a sum of distinct elements of the set outside $B$. This is the case $p(x)=x^2$ of Problem 351. Van Doorn posted the result in the problem's thread on 2025-09-15 with a write-up in their repository of mathematical notes, pinned above at the commit of that day. The proof combines the proof of Theorem 2 of Graham's 1963 paper (the card Graham 1963) with Alekseyev's theorem that every large integer is a sum of distinct squares whose reciprocals sum to one (the card Alekseyev 2019); the post describes the write-up as essentially Graham's proof adapted. The post also records that Graham asked the same question for $n^2+1/n$ in his 1971 paper on sums of integers taken from a fixed sequence.

Covers. The polynomial $p(x)=x^2$ only. The case $p(x)=x$ is Graham's theorem, and the general case is the full claim on the Price–Barreto page.

Depends on. Nothing in this wiki; the note rests on the two cited papers.

Standing. Claimed. The note is unrefereed and has no arXiv posting, no formalization and no independent review. The site's remarks credit van Doorn with the positive solution for $p(n)=n^2$, but the site's label, PROVED (LEAN), settles the whole problem through Barreto's observation that it follows from Problem 283, not through this note, so no reviewed evidence is listed. The proof is not compiled in this corpus.