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Some generalizations of the \(S_ n\) sequence of Shanks. (English) Zbl 0842.11004
The author calculates the continued fraction expansion of \(\sqrt {N}\) for the two-parametric series \(N= [\sigma (qr a^n+ \mu(a^k+ \lambda)/ q)/2 ]^2- \sigma^2 \mu\lambda a^n r\), where \(\lambda,\mu\in \{\pm 1\}\), \(qr\mid a^k+\lambda\), \(n>k \geq 1\), \((n,k)= 1\) and \(\sigma\in \{1, 2\}\). Essential special cases where treated by T. Azuhata [Tokyo J. Math. 10, 259-270 (1987; Zbl 0659.12008)] and the reviewer [Abh. Math. Semin. Univ. Hamb. 59, 157-169 (1989; Zbl 0764.11009)].
MSC:
11A55 Continued fractions
11R27 Units and factorization
11R29 Class numbers, class groups, discriminants
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