# Back, Bigger, Better, Stronger

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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