\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
  1. Determine, according to the values of \(n \in \mathbb{N}\), the remainder of the Euclidean division of \(2^n\) by 5. You may present your results in a congruence table.
  2. Deduce the remainder of the Euclidean division of \(1\,357^{2\,017}\) by 5.

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