A Note on Arithmetic Progressions on Quartic Elliptic Curves

被引：0

作者：

Ulas, Maciej ^{[1
]}

机构：

[1] Jagiellonian Univ, Inst Math, Reymonta 4, PL-30059 Krakow, Poland

来源：

JOURNAL OF INTEGER SEQUENCES | 2005年 / 8卷 / 03期

关键词：

elliptic curves; arithmetic progression;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

G. Campbell described a technique for producing infinite families of quartic elliptic curves containing a length-9 arithmetic progression. He also gave an example of a quartic elliptic curve containing a length-12 arithmetic progression. In this note we give a construction of an infinite family of quartics on which there is an arithmetic progression of length 10. Then we show that there exists an infinite family of quartics containing a sequence of length 12.

引用

页数：5