On the family of Thue equation|x 3+mx2y−(m+3)xy2+y3|=k

Abstract

The family of cubic Thue equation which depend on two parameters|x 3+mx2y−(m+3)xy2+y3|=k is studied. Using rational approximation, we give a smaller upper bound of the solution of the equation, that is quite better than the present result. More over we study two inequalities|x 3+mx2y−(m+3)xy2+y3|=k≤2m+3 and|x 3+mx2y−(m+3)xy2+y3|=k≤(2m+3)2 separately. Our result of upper bound make it easy to solve those inequalities by simple method of continuous fraction expansion.

DOI: 10.1007/BF02836648

Cite this paper

@article{Jingbo2008OnTF, title={On the family of Thue equation|x 3+mx2y−(m+3)xy2+y3|=k}, author={Xia Jingbo and Chen Jianhua and Zhang Silan}, journal={Wuhan University Journal of Natural Sciences}, year={2008}, volume={11}, pages={481-485} }