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

IF 0.6 3区数学 Q3 MATHEMATICS

Mathematical Proceedings of the Cambridge Philosophical Society Pub Date : 2023-10-05 DOI:10.1017/s0305004123000488

HUNG M. BUI, KYLE PRATT, ALEXANDRU ZAHARESCU

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引用次数: 0

摘要

摘要Erdős, Graham和Selfridge考虑了对于每一个正整数n， $t_n$的最小值，使得整数$n+1, n+2， \dots, n+t_n $包含一个子集，其与n的成员的乘积是平方。在ABC猜想的假设下，Granville提出了一个关于t_n的大小的开放问题。建立了t_n分布的一些结果，并在此过程中无条件地解决了Granville问题。

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

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, \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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来源期刊

Mathematical Proceedings of the Cambridge Philosophical Society 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Papers which advance knowledge of mathematics, either pure or applied, will be considered by the Editorial Committee. The work must be original and not submitted to another journal.