A note on the Diophantine equation $2^{n-1}(2^{n}-1)=x^3+y^3+z^3$
Number Theory
2017-05-03 v1
Abstract
Motivated by the recent result of Farhi we show that for each the title Diophantine equation has at least two solutions in integers. As a consequence, we get that each (even) perfect number is a sum of three cubes of integers. Moreover, we present some computational results concerning the considered equation and state some questions and conjectures.
Keywords
Cite
@article{arxiv.1705.01074,
title = {A note on the Diophantine equation $2^{n-1}(2^{n}-1)=x^3+y^3+z^3$},
author = {Maciej Ulas},
journal= {arXiv preprint arXiv:1705.01074},
year = {2017}
}