Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/485

 Title: Polynomials of Pellian Type and Continued Fractions Authors: Mollin, R. Keywords: Continued FractionsPell’s EquationPeriod Length Issue Date: 2001 Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences Citation: Serdica Mathematical Journal, Vol. 27, No 4, (2001), 317p-342p Abstract: We investigate infinite families of integral quadratic polynomials {fk (X)} k∈N and show that, for a fixed k ∈ N and arbitrary X ∈ N, the period length of the simple continued fraction expansion of √fk (X) is constant. Furthermore, we show that the period lengths of √fk (X) go to infinity with k. For each member of the families involved, we show how to determine, in an easy fashion, the fundamental unit of the underlying quadratic field. We also demonstrate how the simple continued fraction ex- pansion of √fk (X) is related to that of √C, where √fk (X) = ak*X^2 +bk*X + C. This continues work in [1]–[4]. URI: http://hdl.handle.net/10525/485 ISSN: 1310-6600 Appears in Collections: Volume 27 Number 4

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