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

共 11 条

[1] Rational points on Erdos-Selfridge superelliptic curves
Bennett, Michael A.
Siksek, Samir
[J]. COMPOSITIO MATHEMATICA, 2016, 152 (11) : 2249 - 2254
[2] Integral points on hyperelliptic curves
Bugeaud, Yann
Mignotte, Maurice
Siksek, Samir
Stoll, Michael
Tengely, Szabolcs
[J]. ALGEBRA & NUMBER THEORY, 2008, 2 (08) : 859 - 885
[3] VARIANTS OF ERDOS-SELFRIDGE SUPERELLIPTIC CURVES AND THEIR RATIONAL POINTS
Das, Pranabesh
Laishram, Shanta
Saradha, N.
[J]. MATHEMATIKA, 2018, 64 (02) : 380 - 386
[4] Rational points with large denominator on Erdos-Selfridge superelliptic curves
Saradha, N.
[J]. PUBLICATIONES MATHEMATICAE-DEBRECEN, 2021, 99 (3-4): : 317 - 329
[5] S-INTEGRAL POINTS ON HYPERELLIPTIC CURVES
Gallegos-Ruiz, Homero R.
[J]. INTERNATIONAL JOURNAL OF NUMBER THEORY, 2011, 7 (03) : 803 - 824
[6] COMPUTING INTEGRAL POINTS ON HYPERELLIPTIC CURVES USING QUADRATIC CHABAUTY
Balakrishnan, Jennifer S.
Besser, Amnon
Mueller, J. Steffen
[J]. MATHEMATICS OF COMPUTATION, 2017, 86 (305) : 1403 - 1434
[7] ON PROBLEM OF ERDOS P CONCERNING POINTS WITH INTEGRAL DISTANCES
HARBORTH, H
[J]. ANNALS OF THE NEW YORK ACADEMY OF SCIENCES, 1970, 175 (01) : 206 - &
[8] Computing integral points on genus 2 curves estimating hyperelliptic logarithms
Gallegos-Ruiz, Homero R.
[J]. ACTA ARITHMETICA, 2019, 187 (04) : 329 - 344
[9] Quadratic Chabauty: p-adic heights and integral points on hyperelliptic curves
Balakrishnan, Jennifer S.
Besser, Amnon
Mueller, J. Steffen
[J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2016, 720 : 51 - 79
[10] Jacobian Conjecture as a Problem on Integral Points on Affine Curves
Van Nguyen, Chau
[J]. VIETNAM JOURNAL OF MATHEMATICS, 2022, 50 (01) : 195 - 204

← 1 2 →