I'm trying to prove the following statement

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> There is an integer $n\_0$ such that for any $n\ge n\_0$, in every $9$-coloring of $\{1,2,3,\dots,n\}$, one of the $9$ color classes contains $4$ integers $a,b,c,d$ such that $a+b+c=d$.
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I thought about taking $\{1,2,\dots,n\}$ to be vertices of a graph where edges connect vertices of the same color. Then I tried to use Ramsey theorem, but to no avail. I thought also about Schur theorem and tried to find some generalization of it, but got nothing.

How should one prove the statement?

Please help, thanks!