论文标题

Diophantine方程$ n(x^4+y^4)= z^4+w^4 $

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

论文作者

Tomita, Seiji, Couto, Oliver

论文摘要

2016年,Izadi和Nabardi(B)显示(4-2-4)具有无限的整数解决方案。他们使用了特定的一致数椭圆曲线。 2020年,Ajai Choudhry,Iliya Bluskov和Alexander James(A)表明,方程(4-2-4)具有无限的许多参数解决方案。他们给出了N = 17,257,626,641,706,1921的数字解决方案。

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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