# Lucas Numbers?

Algebra Level 4

$\sqrt[8]{2207-\dfrac{1}{2207-\dfrac{1}{2207-\cdots}}}$

The express above can be expressed as $$\dfrac{a+b\sqrt{c}}{d}$$, where $$a,b,c,d\in \Bbb{Z}$$ with $$\gcd(a, b, d) = 1$$ and $$c$$ is a square free integer. Find the value of $$a + b + c + d$$.

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