Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Perfect powers that are sums of consecutive cubes   Euler noted the relation $6^3=3^3+4^3+5^3$ 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.

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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an