Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complete solutions of certain Lebesgue-Ramanujan-Nagell type equations   It is well-known that for $p=1, 2, 3, 7, 11, 19, 43, 67, 163$, the class
number of $\mathbb{Q}(\sqrt{-p})$ is one. We use this fact to determine all the
solutions of $x^2+p^m=4y^n$ in non-negative integers $x, y, m$ and $n$.

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The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: cs