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Construction of families of long continued fractions. (English) Zbl 1047.11012
Summary: In this survey article, we revisit the construction of simple continued fractions of quadratic irrationals with long period lengths, which has generated much interest in the relatively recent literature. We show that new and not-so-new results actually follow from results of O. Perron [Die Lehre von den Kettenbrüchen, Vol. 1, Stuttgart: Teubner (1954; Zbl 0056.05901)] in the 1950s and from results of this author from over a decade ago. Moreover, we are able to generalize and simplify numerous such results for a better understanding of the phenomenon.

MSC:
11A55 Continued fractions
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