Algebra Level 5

$\large \sqrt[8]{527 - \dfrac{1}{527 - \frac{1}{527 - \cdots}}} = \dfrac{\sqrt{a} + \sqrt{b}}{c} ,$

where $$a,b,c$$ are positive, square-free integers. Find the product $$abc$$.

Details and Assumptions:

• To clarify, it is the $$8^\text{th}$$ root that is being taken.
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