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Erd\H{o}s, Graham, and Selfridge considered, for each positive integer $n$,the least value of $t_n$ so that the integers $n+1, n+2, \dots, n+t_n $ containa subset the product of whose members with $n$ is a square. An open problemposed by Granville concerns the size of $t_n$, under the assumption of the ABCConjecture. We establish some results on the distribution of $t_n$, and in theprocess solve Granville's problem unconditionally.

A problem of Erd\H{o}s-Graham-Granville-Selfridge on integral points on hyperelliptic curves