# Hints Homework 9

**Problem 1**

First argue that it suffices to prove the result for of the form . Then proceed by induction: Assume is a permutation of that does not contain a monotone -AP. Consider the sequence .

**Problem 2**

Choose and a prime number . Consider the set

**Problem 3**

Find a way how you can identify with , so that a line in can be identified with an -dimensional subspace of . Then apply the Hales-Jewett Theorem.

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