A new diophantine equation involving fifth powers
Volume 202 / 2022
Acta Arithmetica 202 (2022), 43-53
MSC: Primary 11D41.
DOI: 10.4064/aa210419-4-7
Published online: 26 November 2021
Abstract
We obtain two parametric solutions 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.
