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Claim. W. van Doorn, On the length of an interval that contains distinct multiples of the first $n$ positive integers, Integers 26 (2026), #A7 (received 19 February 2025, accepted 27 November 2025, published 5 January 2026, the page name's date; also arXiv:2601.16972v1). Its Theorem 1 states that for all large enough $n$,

$$\max_mf(n,m)-f(n,n)>0.36\,n\frac{\log n}{\log\log n},$$

with $f(n,m)$ the least integer such that $(m,m+f(n,m)]$ contains distinct $a_1,\ldots,a_n$ with $i\mid a_i$; the site's open interval $(m,m+f(n,m))$ makes every $f(n,m)$ one larger and leaves the difference unchanged. So the second question of Problem 711, Erdős's unproved (6) of 1992, $\max_m(f(n,m)-f(n,n))\to\infty$, is answered yes in this quantitative form, and the theorem's second sentence restates it: for all large $n$ there is an interval of length $0.36\,n\log n/\log\log n$ that contains no distinct multiples of $1,2,\ldots,n$. The proof is half a page: an elementary shift lemma, $kn+f(kn,kn)\le k^2n+f(n,k^2n)$ for all $k,n$, combined with the Erdős–Pomerance bounds $(2/\sqrt e+o(1))\,n\sqrt{\log n/\log\log n}<f(n,n)<(2+o(1))\,n\sqrt{\log n}$ at $k=\lceil0.6\sqrt{\log n/\log\log n}\rceil$. The library's result page records the statement, the two lemmas and the proof pointer; nothing is independently reviewed by this project.

Covers. The second question only. The first question, the conjectured $\max_mf(n,m)\le n^{1+o(1)}$, is untouched: the theorem gives the lower bound $\max_mf(n,m)\gg n\log n/\log\log n$, which is consistent with the conjecture and far below the published upper bound $n^{3/2}$.

Acceptance. Refereed: published in Integers, a refereed journal, with the dates above. The site's curator's commentary (page last edited 11 January 2026) records the paper's affirmative answer to the second question, after a thread comment of 6 January 2026 announcing the journal reference; the site's label OPEN attaches to the pair of questions and is not acceptance evidence. Nothing here is this project's own review.

Depends on. Erdős and Pomerance (1980), Theorem 2 and Erdős and Pomerance (1980), Theorem 3.