Displaying similar documents to “Some Diophantine approximation results concerning linear recurrences”

Polynomials of Pellian Type and Continued Fractions

Mollin, R. (2001)

Serdica Mathematical Journal

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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...