Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Searching for Diophantine quintuples   We consider Diophantine quintuples $\{a, b, c, d, e\}$. These are sets of
distinct positive integers, the product of any two elements of which is one
less than a perfect square. It is conjectured that there are no Diophantine
quintuples; we improve on current estimates to show that there are at most
$1.18\cdot 10^{27}$ Diophantine quintuples.

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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph