Diophantine Equation $n(x^4+y^4)=z^4+w^4$

Seiji Tomita; Oliver Couto

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arXiv · 2208.10088

Diophantine Equation $n(x^4+y^4)=z^4+w^4$

Seiji Tomita·Oliver Couto

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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.

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Seiji Tomita, Oliver Couto. 2022-07-10. Diophantine Equation $n(x^4+y^4)=z^4+w^4$. https://arxiv.org/abs/2208.10088

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