论文标题
Mordell曲线上积分点的倍数
Multiples of integral points on Mordell curves
论文作者
论文摘要
令$ b $为第六强整数，而$ p $是mordell曲线$ e_b上的非扭转点：y^2 = x^3+b $。在本文中，我们研究了积分倍数$ [n] p $ $ p $。除其他结果外，我们还表明，$ p $最多具有三个积分倍数，$ n> 1 $。从某种意义上说，这个结果很敏锐，$ p $，恰好三个积分倍数$ [n] p $和$ n> 1 $。作为应用程序，我们讨论了等级1 mordell曲线的准最小模型的积分点的数量。
Let $B$ be a sixth-power-free integer and $P$ be a non-torsion point on the Mordell curve $E_B:y^2=x^3+B$. In this paper, we study integral multiples $[n]P$ of $P$. Among other results, we show that $P$ has at most three integral multiples with $n>1$. This result is sharp in the sense that there are points $P$ with exactly three integral multiples $[n]P$ and $n>1$. As an application, we discuss the number of integral points on the quasi-minimal model of rank 1 Mordell curves.
