@article{article_964819, title={On quartic Diophantine equations with trivial solutions in the Gaussian integers}, journal={International Electronic Journal of Algebra}, volume={31}, pages={134–142}, year={2022}, DOI={10.24330/ieja.964819}, author={Ahmadı, Mahnaz and Janfada, Ali S.}, keywords={Diophantine equation, elliptic curves, quartic equation, number of solutions of Diophantine equations}, abstract={We show that the quartic Diophantine equations $ax^4+by^4=cz^2$ has only trivial solution in the Gaussian integers for some particular choices of $a,b$ and $c$. Our strategy is by elliptic curves method. In fact, we exhibit two null-rank corresponding families of elliptic curves over Gaussian field. We also determine the torsion groups of both families.}, number={31}, publisher={Abdullah HARMANCI}