\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
  1. Show that \(4^{28} - 1\) is divisible by 29.
  2. Show that for any \(n \in \mathbb{N}\), \(4^n - 1\) is divisible by 3.
  3. Show that for any \(k \in \mathbb{N}\), \(4^{4k} - 1\) is divisible by 5 and by 17.
  4. Deduce four prime divisors of \(4^{28} - 1\).

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