# A new diophantine equation involving fifth powers

@article{Choudhry2021AND, title={A new diophantine equation involving fifth powers}, author={Ajai Choudhry and Oliver Couto}, journal={Acta Arithmetica}, year={2021} }

In this paper we obtain a parametric solution of the hitherto unsolved diophantine equation (x 1 + x 2 )(x 3 + x 4 ) = (y 1 + y 2 )(y 3 + y 4 ). Further, we show, using elliptic curves, that there exist infinitely many parametric solutions of the aforementioned diophantine equation, and they can be effectively computed. Mathematics Subject Classification 2020: 11D41

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