Refined upper bounds on Schur-like numbers

Swaroop Hegde, Andrew Lott, Giorgis Petridis +1

For positive integers $r,m$ and $N$, every $r$-coloring of $\{1,\dots ,N\}$ contains a monochromatic solution to $x_1+\cdots +x_{m+1}=y_1+\cdots +y_m$ provided that $N \ge 3^r (r!)^{…