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Claim. For every $j\geq 3$ there are infinitely many collections of $j$ pairwise disjoint blocks of four consecutive integers whose product is a square (Theorem 2.2 of the paper); the new cases are $j=3$ and $j=5$, which Ulas had left open. The authors believe, without proof, that these three-block families are minimal in the number of blocks among counterexamples, and they guess that two blocks of length at least four give only finitely many solutions, citing an unpublished abc-based argument of Walsh as support for the case of two blocks of four. Theorem 2.1 of the paper gives infinitely many solutions when one block has length $2$ or two blocks have length $3$, cases the question excludes. Each infinite family answers the question of Problem 363 in the negative. The result is Mark Bauer and Michael A. Bennett, On a question of Erdős and Graham, Enseign. Math. (2) 53 (2007), 259--264, held as the library card records; the record gives only the year, so the page is dated by the year's first day. The first link is the journal volume's record and the second is the paper's file on the second author's publications page. That publications page dates the paper 2008, while the journal's record places it in volume 53, the 2007 volume, and the print itself carries no publication year; the page keeps the journal's year.

Depends on. Theorem 2.2 covers $j=4$ and $j\geq 6$ through Ulas's theorem; the cases $j=3$ and $j=5$ are proved in the paper, and each of them disproves the statement on its own.

Argument, in outline. The proofs exhibit explicit parametrized families of integral points on the hypersurfaces defined by the product equation, extending the polynomial identities Ulas used.

Acceptance. The result appeared in a refereed journal in 2007, the refereed evidence. The site's curator, Thomas Bloom, credits Bauer and Bennett in the problem's commentary with the cases $n=3$ and $n=5$ of blocks of four: that curator credit is the reviewed evidence. Bennett and Van Luijk's 2012 paper (card) builds on the method, but as the second author's own later work it is not independent review. Ulas's earlier disproof is his own claim page.