Consider the following arithmetic sequence \(\{a_n\}_{n=1}^\infty\) of positive integers:

\[10000, 10103, 10206, \cdots{ } \cdots{ } \cdots{ }\]

Find the smallest positive integer \(m\), for which there exists at least one positive integer \(n\) (with \(n<m\)) such that \[a_m \equiv a_n (\mod{ }2017).\].

**Note**:

- You may decide whether to solve Didn't I See You Before? first. Decide at your own risk.

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