# 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.

×