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arXiv · 2509.21948

Non-periodicity of the sequence of the last nonzero digits of factorials and its applications to transcendence

Kohta Gejima·Fumichika Takamizo
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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.

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Kohta Gejima, Fumichika Takamizo. 2025-10-01. Non-periodicity of the sequence of the last nonzero digits of factorials and its applications to transcendence. https://arxiv.org/abs/2509.21948

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