Rational points with large denominator on Erdos-Selfridge superelliptic curves

被引：1

作者：

Saradha, N. ^{[1
,2
]}

机构：

[1] Univ Mumbai, DAE Ctr Excellence Basic Sci, Mumbai 400098, Maharashtra, India

[2] B-706,Everard Towers,Eastern Express Highway, Mumbai 400022, Maharashtra, India

来源：

PUBLICATIONES MATHEMATICAE-DEBRECEN | 2021年 / 99卷 / 3-4期

关键词：

superelliptic curves; rational solutions; exponential Diophantine equations; perfect powers in arithmetic progression; PERFECT POWERS; CONSECUTIVE TERMS; PRODUCTS; VARIANTS;

D O I：

10.5486/PMD.2021.8860

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In 2016, Bennett and Siksek showed that if the Erdos-Selfridge curve (x + 1) ... (x + k) = y(l), k >= 3, l prime, has a rational solution in x and y, then l <= e(3k). In this paper, we show that if there exists a positive rational solution on the above curve, then either the denominator of the solution is large or l <= k.

引用

页码：317 / 329

页数：13

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