Non-periodicity of the sequence of the last nonzero digits of factorials and its applications to transcendence
Abstract
We prove that the sequence of the last nonzero digits of factorials in every integer base $b>2$ is not eventually periodic. We also extend the Adamczewski-Bugeaud criterion, originally formulated for integer base expansions, to Cantor base expansions associated with a periodic Cantor base. As an application, we show that a certain real number expressed through a Cantor base expansion is transcendental when the Cantor base and the digit sequence satisfy suitable conditions.
Fields of Study & Subjects
Analytic Number Theory Research
Mathematical Dynamics and Fractals
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- Functiones et Approximatio Commentarii Mathematici
- Volume
- -1
- Issue
- -1
- Pages
- 1–20
- Publication date
- 1 January 2026
- Language
- EN