Rational points on Erdos-Selfridge superelliptic curves

被引：8

作者：

Bennett, Michael A. ^{[1
]}

Siksek, Samir ^{[2
]}

机构：

[1] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada

[2] Univ Warwick, Inst Math, Coventry CV4 7AL, W Midlands, England

来源：

COMPOSITIO MATHEMATICA | 2016年 / 152卷 / 11期

基金：

英国工程与自然科学研究理事会; 加拿大自然科学与工程研究理事会;

关键词：

superelliptic curves; Galois representations; Frey curve; modularity; level lowering; CONSECUTIVE TERMS; PRODUCTS; POWERS; FORMS;

D O I：

10.1112/S0010437X16007569

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given k >= 2, we show that there are at most finitely many rational numbers x and y not equal 0 and integers l >= 2 (with (k, l) not equal (2, 2)) for which x(x + 1) center dot center dot center dot (x + k - 1) = y(l). In particular, if we assume that is prime, then all such triples (x, y,l) satisfy either y = 0 or l < exp(3(k)).

引用

页码：2249 / 2254

页数：6

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