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The Van der Waerden number $w(l,k)$ is the least $n$ such that for every $k$-coloring of $[n]$ has a monochromatic $l$-term arithmetic progression. Prove that $w(l,k)>(lk^{l-1})^{1/2}$

Give some hints.

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This looks like a job for the probabilistic method. – Chris Eagle Jan 29 '13 at 19:10
    
Yes, what's more details? – user60134 Jan 29 '13 at 19:13
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The question begs for a please... – Sasha Jan 29 '13 at 19:14
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What makes you think I have any more details? And what happened to wanting "hints"? – Chris Eagle Jan 29 '13 at 19:14

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