A new diophantine equation involving fifth powers

Ajai Choudhry, Oliver Couto

In this paper we obtain a parametric solution of the hitherto unsolved diophantine equation $(x_1^5+x_2^5)(x_3^5+x_4^5)=(y_1^5+y_2^5)(y_3^5+y_4^5)$. Further, we show, using ellipti…