Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Conjecture Connected with Units of Quadratic Fields   In this article, we consider the order $\mathcal{O}_{f}={x+yf\sqrt{d}:x,\ y
\in \Z}$ with conductor $f\in\N$ in a real quadratic field
$K=\mathbb{Q}(\sqrt{d})$ where $d>0$ is square-free and $d\equiv2,3\pmod 4$. We
obtain numerical information about $ n(f)=n(p)=min{\nu\in\N :
\varepsilon^{\nu}\in \mathcal{O}_{p}}$ where $\varepsilon>1$ is the fundamental
unit of $K$ and $p$ is an odd prime. Our numerical results suggest that the
frequencies of $\frac{p\pm1}{2n(p)}$ or $\frac{p\pm1}{n(p)}$ should have a
limit as the ranges of $d$ and $p$ go to infinity.

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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
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The categories of this paper are: hep-th
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The categories of this paper are: supr-con
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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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: dg-ga
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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: nucl-th