arXiv subjects
Publications and source records attributed to Hongshen Chua.
In this paper, we introduce a matrix-based binary tree that forms the foundation of both the Stern--Brocot and Calkin--Wilf trees. We then explore its connection to continued fractions. Building on this relationship, we provide a path-based representation of Brillhart's proof of the sum of two squares.
This paper introduces a variation on an identity by Bruckman and Good. Using this identity, we are able to derive various well-known sums involving reciprocals of Fibonacci and Lucas numbers, including the case when the indices form an arithmetic progression. Moreover, we provide generalizations of the Millin series.
This paper presents a reinterpretation of a second-order linear recurrence sequence as a sequence of continuants derived from the convergents to a continued fraction. As a result, we are able to derive the generating function and Binet formula for continuants. Using this result, we provide a continuant-based formulation for well-known identities associated with Lucas sequences.