Waring's problem with restricted digits
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866913579425333248 |
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| author | Green, Ben |
| author_facet | Green, Ben |
| contents | Let $k \geq 2$ and $b \geq 3$ be integers, and suppose that $d_1, d_2 \in \{0,1,\dots, b - 1\}$ are distinct and coprime. Let $\mathcal{S}$ be the set of non-negative integers, all of whose digits in base $b$ are either $d_1$ or $d_2$. Then every sufficiently large integer is a sum of at most $b^{160 k^2}$ numbers of the form $x^k$, $x \in \mathcal{S}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_09383 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Waring's problem with restricted digits Green, Ben Number Theory Let $k \geq 2$ and $b \geq 3$ be integers, and suppose that $d_1, d_2 \in \{0,1,\dots, b - 1\}$ are distinct and coprime. Let $\mathcal{S}$ be the set of non-negative integers, all of whose digits in base $b$ are either $d_1$ or $d_2$. Then every sufficiently large integer is a sum of at most $b^{160 k^2}$ numbers of the form $x^k$, $x \in \mathcal{S}$. |
| title | Waring's problem with restricted digits |
| topic | Number Theory |
| url | https://arxiv.org/abs/2309.09383 |