JP Journal of Algebra, Number Theory and Applications
Volume 2, Issue 1, Pages 47 - 60
(April 2002)
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PELLIAN POLYNOMIALS AND PERIOD LENGTHS OF CONTINUED FRACTIONS
R. A. Mollin (Canada), K. Cheng (Canada) and B. Goddard (USA)
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Abstract: We investigate integral
polynomials of the form
where
and provide infinite families wherein the
period length of the simple continued fraction
expansion of
is fixed and independent of X for
given A, B, C.
Furthermore, we show that by a judicious
choice of A, B, C, we
may produce period lengths of
that are bigger than any given
This corrects attempts at so doing in [Acta
Arith. 89 (1999), 23-35], and provides a more
general result than that intended therein.
This also continues work in [Indian J. Pure
Appl. Math. 28 (1997), 429-438]. |
Keywords and phrases: continued fractions,
Pell’s equation, period length. |
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