\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Let \(n \in \mathbb{N}^*\). We denote \(a = n^{13} - n\).
  1. Show that \(a\) is divisible by \(13\) and by \(7\).
  2. Deduce that \(a\) is divisible by \(182\).

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