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 50 consecutive cubes. We generalize Stroeker's work by determining all perfect powers that are sums of at most 50 consecutive cubes. Our methods include descent, linear forms in two logarithms and Frey-Hellegouarch curves.
Original language | English |
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Pages (from-to) | 230-249 |
Number of pages | 20 |
Journal | Mathematika |
Volume | 63 |
Issue number | 1 |
DOIs | |
Publication status | Published - 5 Oct 2016 |