arXiv: Number Theory | 2019
Some more Long Continued Fractions, I
Abstract
In this paper we show how to construct several infinite families of polynomials $D(\\bar{x},k)$, such that $\\sqrt{D(\\bar{x},k)}$ has a regular continued fraction expansion with arbitrarily long period, the length of this period being controlled by the positive integer parameter $k$. We also describe how to quickly compute the fundamental units in the corresponding real quadratic fields.