Erdős, 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 $ contain a subset the product of whose members with n is a square. An open problem posed by Granville concerns the size of $t_n$, under the assumption of the ABC conjecture. We establish some results on the distribution of $t_n$, and in the process solve Granville’s problem unconditionally.

中文翻译：

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超椭圆曲线上积分点的 Erdős-Graham-Granville-Selfridge 问题

Erdős、Graham 和 Selfridge 考虑了，对于每个正整数n ， $t_n$的最小值，使得整数$n+1, n+2, \dots, n+t_n $包含其成员与n的乘积的子集是一个正方形。 Granville 提出的一个开放问题涉及在 ABC 猜想的假设下$t_n$的大小。我们对$t_n$的分布建立了一些结果，并在此过程中无条件地解决了 Granville 问题。