VARIANTS OF ERDOS-SELFRIDGE SUPERELLIPTIC CURVES AND THEIR RATIONAL POINTS

被引：4
|
作者：
Das, Pranabesh [1 ]
Laishram, Shanta [1 ]
Saradha, N. [2 ]
机构：
[1] Indian Stat Inst, Delhi Ctr, Stat Math Unit, New Delhi 110016, India
[2] Tata Inst Fundamental Res, Sch Math, Bombay 400005, Maharashtra, India
来源：
MATHEMATIKA | 2018年 / 64卷 / 02期
关键词：
CONSECUTIVE TERMS; PERFECT POWERS; PRODUCTS;
D O I：
10.1112/S0025579317000559
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
For the superelliptic curves of the form (x + 1) center dot center dot center dot (x + i - l)(x + i + 1) .center dot center dot (x + k) = y(l) with y not equal 0, k >= 3, l >= 2, a prime and for i epsilon [2, k] backslash Omega, we show that l < e(3k). Here Omega denotes the interval [p theta, (k - p theta)), where p theta is the least prime greater than or equal to k/2. Bennett and Siksek obtained a similar bound for i = 1 in a recent paper.
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页码：380 / 386
页数：7
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