Question 56
Let $\mathbb{N}$ denote the strictly positive integers. A function $f : \mathbb{N} \to \mathbb{N}$ satisfies the following for all $n \in \mathbb{N}$:
$$
\begin{aligned}
f(1) &= 1 \\
f(f(n)) &= n \\
f(2n) &= 2f(n) + 1.
\end{aligned}
$$
Find the value of $f(2020)$.
$$
\begin{aligned}
f(1) &= 1 \\
f(f(n)) &= n \\
f(2n) &= 2f(n) + 1.
\end{aligned}
$$
Find the value of $f(2020)$.