Non-periodicity of the sequence of the last nonzero digits of factorials and its applications to transcendence
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911186886328320 |
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| author | Gejima, Kohta Takamizo, Fumichika |
| author_facet | Gejima, Kohta Takamizo, Fumichika |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_21948 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-periodicity of the sequence of the last nonzero digits of factorials and its applications to transcendence Gejima, Kohta Takamizo, Fumichika Number Theory 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. |
| title | Non-periodicity of the sequence of the last nonzero digits of factorials and its applications to transcendence |
| topic | Number Theory |
| url | https://arxiv.org/abs/2509.21948 |