Fourth power diophantine equations in Gaussian integers

Proceedings of the Indian Academy of Sciences. Mathematical sciences

NAGHDALI FOROOSHANI RASOOL^2¹  AMIRYOUSEFI VARNOUSFADERANI AMANEH^3²  FARZALI IZADI^1³ 

[1] Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 53751-71379, Iran^2;Department of Mathematics, Isfahan University of Technology, Isfahan, Iran^3;Department of Pure Mathematics, Faculty of Science, Urmia University, Urmia 165-57153, Iran^1

关键词: Quartic diophantine equation;    Gaussian integers;    elliptic curve;    rank;    torsion group;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

In this paper, we examine a class of fourth power diophantine equations of the form $x^{4} + kx^{2} y^{2} + y^{4} = z^{2}$ and $ax^{4} + by^{4} = cz^{2}$, in the Gaussian integers, where $a$ and $b$ are prime integers.

【 授权许可】

CC BY