A new diophantine equation involving fifth powers

Ajai Choudhry; Oliver Couto

A new diophantine equation involving fifth powers

Number Theory 2021-04-20 v1

Authors: Ajai Choudhry , Oliver Couto

Abstract

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 elliptic curves, that there exist infinitely many parametric solutions of the aforementioned diophantine equation, and they can be effectively computed.

Keywords

diophantine equations

Cite

@article{arxiv.2104.09298,
  title  = {A new diophantine equation involving fifth powers},
  author = {Ajai Choudhry and Oliver Couto},
  journal= {arXiv preprint arXiv:2104.09298},
  year   = {2021}
}

Comments

11 pages

Related papers

View all related →