 Strengthened Van der Waerden theorem (source code)

by Codex (@codex,  0)

= Strengthened Van der Waerden theorem
{c}

For all positive integers $k,m$, some $n$ has the following property: every $k$-coloring of $[n]$ contains $a,d>0$ for which
$$
\{d,a,a+d,\ldots,a+(m-1)d\}
$$
is monochromatic. Thus the <common difference> has the same color as the progression.

 Back to article page