# Number base and binomial coefficient

$\overline{C_{0}^{0} } _{x} + \overline{C_{0}^{1} C_{1}^{1}} _{x} + \overline{C_{0}^{2} C_{1}^{2} C_{2}^{2}} _{x} + \cdots + \overline{C_{0}^{2016} \dots C_{2016}^{2016}}_{x} = \underbrace{\overline{111\dots111}_{(x+1)}}_{2017 \ 1's}$

Find the minimum possible value of $$x$$ which satisfies the equation above. (Note: The number base must be positive integer.)

Notation: $$\large C_{k}^{n}= { n \choose k } = \frac{n!}{k!(n-k)!}$$ denotes of binomial coefficient.

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