Abstract
We give a description of the cubic polynomials f(x) with coefficients in the quadratic number fields \(\mathbb{Q}(\sqrt{5})\) and \(\mathbb{Q}(\sqrt{-15})\) for which the continued fraction expansion of the irrationality \(\sqrt {f\left( x \right)} \) is periodic.
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Original Russian Text © V.P. Platonov, V.S. Zhgoon, G.V. Fedorov, 2018, published in Doklady Akademii Nauk, 2018, Vol. 482, No. 2.
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Platonov, V.P., Zhgoon, V.S. & Fedorov, G.V. On the Periodicity of Continued Fractions in Hyperelliptic Fields over Quadratic Constant Field. Dokl. Math. 98, 430–434 (2018). https://doi.org/10.1134/S1064562418060091
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DOI: https://doi.org/10.1134/S1064562418060091