Periodicity in radix systems with base 3
Publication Name: Publicationes Mathematicae Debrecen
Publication Date: 2025-01-01
Volume: 106
Issue: 3-4
Page Range: 475-489
Description:
In this paper, we examine the base 3 number expansions in the ring of integers with digits {0, a, −b}, a, b ∈ N and a ≡ b (mod 3). Among others, we show that for arbitrary natural numbers n and k, there is a system where n has a periodic expansion with length k. We specify an infinite number of radix systems for a given valid signature.
Open Access: Yes
