A binary additive equation with prime and square-free number
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912633779650560 |
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| author | Dimitrov, S. I. |
| author_facet | Dimitrov, S. I. |
| contents | Let $[\, \cdot\,]$ be the floor function. In this paper, we show that when $1<c<\frac{82}{79}$, then every sufficiently large positive integer $N$ can be represented in the form \begin{equation*} N=[p^c]+[m^c]\,, \end{equation*} where $p$ is a prime and $m$ is a square-free. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06190 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A binary additive equation with prime and square-free number Dimitrov, S. I. Number Theory Let $[\, \cdot\,]$ be the floor function. In this paper, we show that when $1<c<\frac{82}{79}$, then every sufficiently large positive integer $N$ can be represented in the form \begin{equation*} N=[p^c]+[m^c]\,, \end{equation*} where $p$ is a prime and $m$ is a square-free. |
| title | A binary additive equation with prime and square-free number |
| topic | Number Theory |
| url | https://arxiv.org/abs/2401.06190 |