Szemeredi's Theorem is a famous theorem in Additive Combinatorics, Ergodic Theory and maybe some other parts of Mathemtatics:

(Szemeredi's Theorem) Let $\Lambda \in \mathbb{Z}$ be a subset of integers of positive upper density, then $\Lambda$ contains arbitrary long arithmetic progressions.

As I know, the techniques used for prooving the Szemeredi's Theorem are important in Mathematics.

My Questions is this:

- Do you have any example of interesting or important problems that can be solved with Szemeredi's Theorem? (I know that Green-Tao Theorem is one of famous theorems, Szemeredi's Theorem used in solving it.)