Function Game

Algebra Level 4

\[\large \begin{cases} f(1)=1 \\ f(2n)=n \; f(n) \end{cases} \]

Let \(f : \mathbb N \to \mathbb N\) be a function satisfying the above properties. Find \(f(2^{100}) \).

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

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