Sums, products, and exponents in two-colorings of the naturals
Ryan Alweiss, Matthew Bowen, Marcin Sabok·2025-12-10·via math.CO updates on arXiv.org
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 $k$.