Algebraic Integers with Continued Fraction Expansions Containing Palindromes and Square Roots with Prescribed Periods
Abstract
We present a characterization of the algebraic integers with continued fraction expansions of the form [a0,a1,…,an,s¯], where (a1,…,an) is a palindrome and s∈N≥1. In particular, we focus on the special case where (a1,…,an)=(m,…,m), providing detailed characterizations of the corresponding algebraic integers and s in terms of Fibonacci polynomials. Then, we derive new expansions of square roots of integers with these periods, given m and n. Moreover, we explicitly determine the fundamental solutions of both positive and negative Pell’s equations corresponding to this family of integers.
Fields of Study & Subjects
Matrix Theory and Algorithms
Polynomial and algebraic computation
Mathematical functions and polynomials
Publication details
- Journal / source
- The Fibonacci Quarterly
- Volume
- 64
- Issue
- 2
- Pages
- 221–235
- Publication date
- 6 January 2026
- Language
- EN