A new diophantine equation involving fifth powers

2021/04/13 by Choudhry, Ajai, Couto, Oliver
#11D41 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2104.09298

Abstract

In this paper we obtain a parametric solution of the hitherto unsolved diophantine equation (x₁⁵+x₂⁵)(x₃⁵+x₄⁵)=(y₁⁵+y₂⁵)(y₃⁵+y₄⁵). Further, we show, using elliptic curves, that there exist infinitely many parametric solutions of the aforementioned diophantine equation, and they can be effectively computed.

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