The site's wording fails on the diagonal $m=n$, where the two sets coincide: the intersection is then $\{k(n-k):1\le k\le n/2\}$ itself, with $\lfloor n/2\rfloor$ elements, so it is trivially arbitrarily large and is not $(mn)^{o(1)}=n^{o(1)}$, and the third question has the trivial answer no. The failure is this page's own elementary check. The change inserts "with $m\neq n$" after "Let $m,n\geq 1$"; nothing else changes. Since the intersection is symmetric in $m$ and $n$, the corrected question is the same as the one for $m>n$. The evidence is first the poser's own words: Erdős and Graham [ErGr80, p. 88] consider "the two sets" and ask whether the number of integers common to both is unbounded, adding that it "should certainly be less than $(mn)^\varepsilon$ for every $\varepsilon>0$ if $mn$ is sufficiently large"; on the diagonal the two sets are one, the unboundedness is immediate and the bound is false, so these words fit only distinct $m$ and $n$: the poser's text assumes two distinct sets, and the slip is the unstated $m\neq n$. The site's commentary, which states the solution for $m>n$, its label PROVED, and the formal-conjectures statement listed under Formalization, which assumes $n<m$ in both its parts, agree with the change but do not license it: their restriction is Hegyvári's hypothesis. The defect is already in the poser's text, which states no restriction on $m$ and $n$. Hegyvári's paper quotes the question without one and proves its theorems for $m>n$; that hypothesis is not the source of the change. No result about the site's wording exists beyond the check recorded here, which settles no instance of the corrected Statement.