Perfect powers that are sums of consecutive cubes

Michael A. Bennett, Vandita Patel, Samir Siksek

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)230-249
Number of pages20
JournalMathematika
Volume63
Issue number1
DOIs
Publication statusPublished - 5 Oct 2016

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