Polynomials of Pellian Type and Continued Fractions

Mollin, 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 -