Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An equivalent condition for the Markov triples and the Diophantine
  equation $a^2+b^2+c^2=abcf(a,b,c)$   We propose an equivalent condition for the Markov triples, which was
mentioned by H. Rademacher essentially. As an application, we study the
solvability of the Diophantine equation $a^2+b^2+c^2=abcf(a,b,c)$.

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The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: physics
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The categories of this paper are: cs
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The categories of this paper are: nucl-th