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Show that \(4^{28} - 1\) is divisible by 29.
Show that for any \(n \in \mathbb{N}\), \(4^n - 1\) is divisible by 3.
Show that for any \(k \in \mathbb{N}\), \(4^{4k} - 1\) is divisible by 5 and by 17.
Deduce four prime divisors of \(4^{28} - 1\).
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