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].
