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arXiv · 2512.09598

Sums, products, and exponents in two-colorings of the naturals

Ryan Alweiss·Matthew Bowen·Marcin Sabok
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Abstract

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 $k$.

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Ryan Alweiss, Matthew Bowen, Marcin Sabok. 2025-12-10. Sums, products, and exponents in two-colorings of the naturals. https://arxiv.org/abs/2512.09598

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