PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

Multiples of integral points on Mordell curves

Volume 211 / 2023

Amir Ghadermarzi Acta Arithmetica 211 (2023), 121-159 MSC: Primary 11G05. DOI: 10.4064/aa220822-3-8 Published online: 16 October 2023


Let $B$ be a sixth-power-free integer and $P$ be a non-torsion point on the Mordell curve $E_B:y^2=x^3+B$. We study the integral multiples $[n]P$ of $P$. Among other results, we show that $P$ has at most three integral multiples with $n \gt 1$. This result is sharp in the sense that there are points $P$ with exactly three integral multiples $[n]P$ and $n \gt 1$. As an application, we discuss the number of integral points on the quasi-minimal model of rank 1 Mordell curves.


  • Amir GhadermarziSchool of Mathematics, Statistics and Computer Science
    College of Science
    University of Tehran
    Tehran, Iran
    School of Mathematics
    Institute of Research in Fundamental Science (IPM)
    Tehran, Iran

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image