# How well do you know $$\sqrt{2017}?$$

Algebra Level 4

$f(x) = \begin{cases} 0 + \beta \ : \ \lfloor x \rfloor \equiv 0 \mod 3 \\ 1 + \beta \ : \ \lfloor x \rfloor \equiv 1 \mod 3 \\ 2 + \beta \ : \ \lfloor x \rfloor \equiv 2 \mod 3 \\ \end{cases}$

There is a unique value of $$\beta$$ such that $\displaystyle \sum_{n=1}^{\infty} \frac{f \left( 3^{n}\sqrt{2017} \right)}{3^{n}} = 0.$ This value of $$\beta$$ can be expressed as $$a-b\sqrt{c},$$ where $$a,\ b,$$ and $$c$$ are positive integers and $$c$$ is square-free. Find $$a + b + c .$$

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