A problem of Erdős-Graham-Granville-Selfridge on integral points on hyperelliptic curves

2022/11/22 by Hung M. Bui, Kyle Pratt, Bui, Hung M. +3 · 1 citation
Arts and Humanities · Mathematics · #Analytic Number Theory Research #FOS: Mathematics #Historical Studies and Socio-cultural Analysis #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2211.12467

openalex publication_date 2022/11/22 · openalex created_date 2022/11/29 · openalex updated_date 2026/07/28

Abstract

Erdős, Graham, and Selfridge considered, for each positive integer n, the least value of t_n so that the integers n+1, n+2, …, 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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