# Number base and binomial coefficient

**Discrete Mathematics**Level 3

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

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.