A number theory problem by Wildan Bagus W. Hafidz

\[\left( \begin{matrix} 2017 \\ 0 \end{matrix} \right) +\left( \begin{matrix} 2017 \\ 1 \end{matrix} \right) +\left( \begin{matrix} 2017 \\ 2 \end{matrix} \right) +...+\left( \begin{matrix} 2017 \\ 2016 \end{matrix} \right) +\left( \begin{matrix} 2017 \\ 2017 \end{matrix} \right) \]

Find the units digit of the number above.

Notations:

  • \(\displaystyle {M \choose N} = \frac {M!}{N!(M-N)!}\) denotes the binomial coefficient.
  • \(!\) denotes the factorial notation; for example: \(8! = 1\times 2 \times 3 \times \cdots \times 8\).
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