# Polynomials of Pellian Type and Continued Fractions

Serdica Mathematical Journal (2001)

- Volume: 27, Issue: 4, page 317-342
- ISSN: 1310-6600

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topMollin, R.. "Polynomials of Pellian Type and Continued Fractions." Serdica Mathematical Journal 27.4 (2001): 317-342. <http://eudml.org/doc/11543>.

@article{Mollin2001,

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].},

author = {Mollin, R.},

journal = {Serdica Mathematical Journal},

keywords = {Continued Fractions; Pell’s Equation; Period Length; continued fractions; Pell's equation; period length},

language = {eng},

number = {4},

pages = {317-342},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {Polynomials of Pellian Type and Continued Fractions},

url = {http://eudml.org/doc/11543},

volume = {27},

year = {2001},

}

TY - JOUR

AU - Mollin, R.

TI - Polynomials of Pellian Type and Continued Fractions

JO - Serdica Mathematical Journal

PY - 2001

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 27

IS - 4

SP - 317

EP - 342

AB - 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].

LA - eng

KW - Continued Fractions; Pell’s Equation; Period Length; continued fractions; Pell's equation; period length

UR - http://eudml.org/doc/11543

ER -

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