Mahler's $\frac{3}{2}$ problem in $\mathbb{Z}^{+} $
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911010990850048 |
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| author | Kumar, Nikhil S |
| author_facet | Kumar, Nikhil S |
| contents | This problem was asked to K. Mahler by one of his Japanese colleagues, a Z-number is a positive real number $x$ such that the fractional parts of $x(\frac{3}{2})^n $ are less than $\frac{1}{2}$ for all integers $n$ such that $n \ge 0$. Kurt Mahler conjectured in 1968 that there are no Z-numbers. In this paper, we show that there are no Z-numbers in $\mathbb{Z}^{+} = \{1,2,3,...\}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_03468 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mahler's $\frac{3}{2}$ problem in $\mathbb{Z}^{+} $ Kumar, Nikhil S Number Theory This problem was asked to K. Mahler by one of his Japanese colleagues, a Z-number is a positive real number $x$ such that the fractional parts of $x(\frac{3}{2})^n $ are less than $\frac{1}{2}$ for all integers $n$ such that $n \ge 0$. Kurt Mahler conjectured in 1968 that there are no Z-numbers. In this paper, we show that there are no Z-numbers in $\mathbb{Z}^{+} = \{1,2,3,...\}$. |
| title | Mahler's $\frac{3}{2}$ problem in $\mathbb{Z}^{+} $ |
| topic | Number Theory |
| url | https://arxiv.org/abs/2411.03468 |