On Rado's single equation theorem
Fuente:
arXiv
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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908899820437504 |
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| author | Sanders, Tom |
| author_facet | Sanders, Tom |
| contents | We show that for non-zero integers $a$ and $b$ there is a natural number $N < \exp(r^{2+o_{a,b;r\rightarrow \infty}(1)})$ such that in any $r$-colouring of $\{1,\dots,N\}$ there are $x,y,z$, all in the same colour class, such that $ax-ay=bz$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_18179 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Rado's single equation theorem Sanders, Tom Combinatorics Number Theory We show that for non-zero integers $a$ and $b$ there is a natural number $N < \exp(r^{2+o_{a,b;r\rightarrow \infty}(1)})$ such that in any $r$-colouring of $\{1,\dots,N\}$ there are $x,y,z$, all in the same colour class, such that $ax-ay=bz$. |
| title | On Rado's single equation theorem |
| topic | Combinatorics Number Theory |
| url | https://arxiv.org/abs/2603.18179 |