Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solving Quadratic and Cubic Diophantine Equations using 2-adic Valuation
  Trees   For fixed integers $D \geq 0$ and $c \geq 3$, we demonstrate how to use
$2$-adic valuation trees of sequences to analyze Diophantine equations of the
form $x^2+D=2^cy$ and $x^3+D=2^cy$, for $y$ odd. Further, we show for what
values $D \in \mathbb{Z}^+$, the numbers $x^3+D$ will generate infinite
valuation trees, which lead to infinite solutions to the above Diophantine
equations.

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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: astro-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: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol