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

被引：0

作者：

Bui, Hung M. ^{[1
]}

Pratt, Kyle ^{[2
]}

Zaharescu, Alexandru ^{[3
]}

机构：

[1] Univ Manchester, Dept Math, Manchester M13 9PL, England

[2] Brigham Young Univ, Dept Math, Provo, UT 84602 USA

[3] Univ Illinois, Dept Math, 1409 West Green St, Urbana, IL 61801 USA

来源：

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY | 2024年 / 176卷 / 02期

关键词：

11N25; 11D41;

D O I：

10.1017/S0305004123000488

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Erdos, 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.

引用

页码：309 / 323

页数：15