In this paper we show how to construct several infinite families of polynomials D(¯x, k), such that p D(¯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.
Institute of Mathematics, Polish Academy of Sciences
McLaughlin, J., & Zimmer, P. (2007). Some more Long Continued Fractions, I. Acta Arithmetica, 127(4), 365-389. Retrieved from https://digitalcommons.wcupa.edu/math_facpub/57