Perfect powers that are sums of consecutive cubes
Number Theory
2019-02-20 v2
Abstract
Euler noted the relation and asked for other instances of cubes that are sums of consecutive cubes. Similar problems have been studied by Cunningham, Catalan, Gennochi, Lucas, Pagliani, Cassels, Uchiyama, Stroeker and Zhongfeng Zhang. In particular Stroeker determined all squares that can be written as a sum of at most consecutive cubes. We generalize Stroeker's work by determining all perfect powers that are sums of at most consecutive cubes. Our methods include descent, linear forms in two logarithms, and Frey-Hellegouarch curves.
Keywords
Cite
@article{arxiv.1603.08901,
title = {Perfect powers that are sums of consecutive cubes},
author = {Michael Bennett and Vandita Patel and Samir Siksek},
journal= {arXiv preprint arXiv:1603.08901},
year = {2019}
}