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Claim. For every $r\geq 5$ there are infinitely many $(r+1)$-tuples $(n_1,\dots,n_r,x)$ of positive integers with $\prod_{j=1}^r n_j(n_j+1)(n_j+2)(n_j+3)(n_j+4)=x^2$ and $n_j+5\leq n_{j+1}$, that is, infinitely many collections of $r$ pairwise disjoint blocks of five consecutive integers whose product is a square (Theorem 1.1 of the paper). Each such family answers the question of Problem 363 in the negative, now with blocks of five rather than four. The result is Michael A. Bennett and Ronald Van Luijk, Squares from blocks of consecutive integers: a problem of Erdős and Graham, Indag. Math. (N.S.) 23 (2012), no. 1--2, 123--127, held as the library card records; the journal record gives the issue as March 2012 and no day, so the page is dated by the first of that month. The second link is the paper's file on the first author's publications page.

Argument, in outline. The authors leave open whether the polynomial-identity and Pell-equation argument that Bauer and Bennett used for blocks of four extends to blocks of five or more. They instead find four polynomials in $\mathbb{Z}[t]$, pairwise distinct up to small shifts, whose product of five-term blocks is $g(t)h(t)^2$ with $g$ quadratic, solve $g(t)=Ds^2$ for suitable squarefree $D$, attach fixed blocks whose product is $D$ times a square, and induct on $r$. The authors note that their techniques appear unlikely to work for blocks of length six or more.

Acceptance. The result appeared in a refereed journal in 2012, the refereed evidence. The site's curator, Thomas Bloom, credits Bennett and Van Luijk in the problem's commentary with the blocks-of-five families for every $n\geq 5$: that curator credit is the reviewed evidence. The disproofs with blocks of four are Ulas's and Bauer and Bennett's.