Diophantine Equation $n(x^4+y^4)=z^4+w^4$
General Mathematics
2022-08-23 v1
Abstract
In 2016 Izadi and Nabardi (b) showed (4-2-4) has infinitely many integer solutions. They used a specific congruent number elliptic curve.In 2019 Janfada and Nabardi,item C, showed that a necessary condition for n to have an integral solution for the above equation and gave a parametric solution.They gave the numeric solutions for n=41,136,313,1028,1201,3281. In 2020 Ajai Choudhry , Iliya Bluskov and Alexander James (a), showed that equation (4-2-4) has infinitely many parametric solutions. They gave the numeric solutions for n=17,257,626,641,706,1921.
Keywords
Cite
@article{arxiv.2208.10088,
title = {Diophantine Equation $n(x^4+y^4)=z^4+w^4$},
author = {Seiji Tomita and Oliver Couto},
journal= {arXiv preprint arXiv:2208.10088},
year = {2022}
}