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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