# Lucas Numbers?

Algebra Level 4

The expression :

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

can be expressed as $$\dfrac{a+b\sqrt{c}}{d}$$ where $$a,b,c,d\in \Bbb{Z}$$.

Find the value of $$a + b + c + d$$.

$$c$$ is a square free integer, $$\gcd(a, b, d) = 1$$.

×