Sums, products, and exponents in two-colorings of the naturals
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909954705719296 |
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| author | Alweiss, Ryan Bowen, Matthew Sabok, Marcin |
| author_facet | Alweiss, Ryan Bowen, Matthew Sabok, Marcin |
| contents | We prove that for any coloring of the naturals using two colors there are monochromatic sets of the form $\{x,y,xy,x+iy:i\leq k\}$ and $\{x,y,x^y,xy^i:i\leq k\}$ for any $k$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_09598 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sums, products, and exponents in two-colorings of the naturals Alweiss, Ryan Bowen, Matthew Sabok, Marcin Combinatorics 05D10, 54D80 We prove that for any coloring of the naturals using two colors there are monochromatic sets of the form $\{x,y,xy,x+iy:i\leq k\}$ and $\{x,y,x^y,xy^i:i\leq k\}$ for any $k$. |
| title | Sums, products, and exponents in two-colorings of the naturals |
| topic | Combinatorics 05D10, 54D80 |
| url | https://arxiv.org/abs/2512.09598 |