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Algebra Level 5

Given a strictly increasing function \(f : \mathbb{N} \to \mathbb{N}\) which satisfies

\[f(f(f(x))) = 4x\]

Find \(f(3171)\).

\[\] Bonus: Generalize this for any strictly increasing function which satisfies \(f : \mathbb{N} \to \mathbb{N}\) and \(f(f( \cdots f(x))) = (n+1)x\), where the function is iterated \(n\) times.

Notation: \(\mathbb N \) denotes the set of natural numbers.

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