A van der Waerden Variant
A van der Waerden Variant
The classical van der Waerden Theorem says that for every every finite set $S$ of natural numbers and every $k$-coloring of the natural numbers, there is a monochromatic set of the form $aS+b$ for some $a>0$ and $b\geq 0$. I.e., monochromatism is obtained by a dilation followed by a translation. …