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Here we present a short proof that the two-color van der Waerden number$w(3,k)$ is bounded from below by $(1-o(1))k^2$. Previous work has alreadyshown that a superpolynomial lower bound holds for $w(3,k)$. However, webelieve our result is still is of interest due to our techniques.

A short proof that $w(3,k) \ge (1-o(1))k^2$