Multiples of integral points on Mordell curves
Amir Ghadermarzi

TL;DR
This paper investigates the number of integral multiples of points on Mordell curves, establishing an upper bound of three such multiples for non-torsion points and exploring implications for integral points on related curves.
Contribution
It proves that non-torsion points on certain Mordell curves have at most three integral multiples, providing a sharp bound and analyzing implications for integral points on rank 1 curves.
Findings
Maximum of three integral multiples for non-torsion points
Existence of points with exactly three integral multiples
Implications for integral points on quasi-minimal models
Abstract
Let be a sixth-power-free integer and be a non-torsion point on the Mordell curve . In this paper, we study integral multiples of . Among other results, we show that has at most three integral multiples with . This result is sharp in the sense that there are points with exactly three integral multiples and . As an application, we discuss the number of integral points on the quasi-minimal model of rank 1 Mordell curves.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Analytic Number Theory Research · Polynomial and algebraic computation
