Binary-ternary collisions and the last significant digit of $n!$ in base 12
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912153614680064 |
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| author | Deshouillers, Jean-Marc Jelinek, Pascal Spiegelhofer, Lukas |
| author_facet | Deshouillers, Jean-Marc Jelinek, Pascal Spiegelhofer, Lukas |
| contents | The third-named author recently proved [Israel J. of Math. 258 (2023), 475--502] that there are infinitely many \textit{collisions} of the base-2 and base-3 sum-of-digits functions. In other words, the equation \[ s_2(n)=s_3(n) \] admits infinitely many solutions in natural numbers. We refine this result and prove that every integer $a$ in $\{1, 2, \ldots, 11\}$ appears as the last nonzero digit of $n!$ in base $12$ infinitely often. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_09124 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Binary-ternary collisions and the last significant digit of $n!$ in base 12 Deshouillers, Jean-Marc Jelinek, Pascal Spiegelhofer, Lukas Number Theory 11A63, 11K31, 11B75 The third-named author recently proved [Israel J. of Math. 258 (2023), 475--502] that there are infinitely many \textit{collisions} of the base-2 and base-3 sum-of-digits functions. In other words, the equation \[ s_2(n)=s_3(n) \] admits infinitely many solutions in natural numbers. We refine this result and prove that every integer $a$ in $\{1, 2, \ldots, 11\}$ appears as the last nonzero digit of $n!$ in base $12$ infinitely often. |
| title | Binary-ternary collisions and the last significant digit of $n!$ in base 12 |
| topic | Number Theory 11A63, 11K31, 11B75 |
| url | https://arxiv.org/abs/2412.09124 |