Bounds for monochromatic solutions to $\{x+y,xy\}$
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912718390296576 |
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| author | Green, Ben Sawhney, Mehtaab |
| author_facet | Green, Ben Sawhney, Mehtaab |
| contents | Let $r$ be a sufficiently large positive integer, and let $N \ge \exp\exp(r^{50})$. Then any $r$-colouring of $[N]$ contains a monochromatic copy of $\{x+y,xy\}$ with $x > y > 2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_09365 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bounds for monochromatic solutions to $\{x+y,xy\}$ Green, Ben Sawhney, Mehtaab Number Theory Combinatorics Let $r$ be a sufficiently large positive integer, and let $N \ge \exp\exp(r^{50})$. Then any $r$-colouring of $[N]$ contains a monochromatic copy of $\{x+y,xy\}$ with $x > y > 2$. |
| title | Bounds for monochromatic solutions to $\{x+y,xy\}$ |
| topic | Number Theory Combinatorics |
| url | https://arxiv.org/abs/2511.09365 |