Question 132
Let $\mathbb{N} = \{1, 2, 3, \dots\}$ be the set of natural numbers.
Consider those functions $f: \mathbb{N} \to \mathbb{N}$ which satisfy the conditions $f(1) = 1$, $f(f(n)) = 3f(n) - 2n$ and $\frac{n-1}{f(n)-n}$ is an integer for $n \ge 2$. Find all possible values of $f(2024)$.
(Nursoltan Khavalbolot)
Consider those functions $f: \mathbb{N} \to \mathbb{N}$ which satisfy the conditions $f(1) = 1$, $f(f(n)) = 3f(n) - 2n$ and $\frac{n-1}{f(n)-n}$ is an integer for $n \ge 2$. Find all possible values of $f(2024)$.
(Nursoltan Khavalbolot)