On some properties of partial quotients of the continued fraction expansion of d with even period

• Published in: Archiv der Mathematik Vol. 114; no. 6; pp. 649 - 660
• Main Authors: Kawamoto, Fuminori, Kishi, Yasuhiro, Tomita, Koshi
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.06.2020; Springer Nature B.V
• Subjects: Mathematics; Mathematics and Statistics; Quotients; Secondary 11R11; 11R29; Primary 11A55; Class numbers; Real quadratic fields; Continued fractions; 11R27

Let d be a non-square positive integer such that the period of the continued fraction expansion of d is even. We give some relations between some properties of partial quotients of the continued fraction expansion of d , which emerge from numerical experiments.