Geodesic
On the sequences of polynomials $f$ with a periodic continued fraction expansion $\sqrt{f}$
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2024), pp. 25-30 
G.V. Fedorov. On the sequences of polynomials $f$ with a periodic continued fraction expansion $\sqrt{f}$. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2024), pp. 25-30. http://geodesic.mathdoc.fr/item/VMUMM_2024_2_a2/
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     title = {On the sequences of polynomials $f$ with a periodic continued fraction expansion $\sqrt{f}$},
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Voir la notice de l'article provenant de la source Math-Net.Ru

For each $n \ge 3$, three nonequivalent polynomials $f \in \mathbb{Q}[x]$ of degree $n$ were previously constructed for which $\sqrt{f}$ has a periodic continued fraction expansion in the field $\mathbb{Q}((x))$. In this paper, for each $n \ge 5$, two new polynomials $f \in K[x]$ of degree $n$ are found, defined over the field $K$, $[K : \mathbb{Q}] = [(n-1)/2]$, for which $\sqrt{f}$ has a periodic continued fraction expansion in the field $K((x))$.

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