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arXiv · 2211.12467

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

Hung M. Bui·Kyle Pratt·Alexandru Zaharescu
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Abstract

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 $ 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.

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Hung M. Bui, Kyle Pratt, Alexandru Zaharescu. 2022-11-22. A problem of Erd\H{o}s-Graham-Granville-Selfridge on integral points on hyperelliptic curves. https://arxiv.org/abs/2211.12467

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