On cubic Thue equations and the common index divisors of cyclic cubic fields

Mohammed Seddik

On cubic Thue equations and the common index divisors of cyclic cubic fields

Number Theory 2018-01-15 v4

Authors: Mohammed Seddik

Abstract

In this paper, we investigate the common index divisors of cyclic cubic fields. Let $a,b,c,d$ and $k$ are integers, we then solve the following Thue cubic equations:: $ax^3+bx^2y+cxy^2+dy^3= k\$ when $a,bc+d$ are odd and $3$ doesn't divide $v_2(k)$ .

Keywords

cyclic cubic fields common index divisors Thue equations cubic forms

Cite

@article{arxiv.1801.02228,
  title  = {On cubic Thue equations and the common index divisors of cyclic cubic fields},
  author = {Mohammed Seddik},
  journal= {arXiv preprint arXiv:1801.02228},
  year   = {2018}
}

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