Question 22
Let $g: \mathbb{N} \to \mathbb{N}$ be a bijective function and suppose that $f: \mathbb{N} \to \mathbb{N}$ is a function such that:
• For all naturals $x$, $f^{x^{2023}}(x) = x$
• For all naturals $x, y$ such that $x \mid y$, we have $f(x) \mid g(y)$.
Prove that $f(x) = x$.
• For all naturals $x$, $f^{x^{2023}}(x) = x$
• For all naturals $x, y$ such that $x \mid y$, we have $f(x) \mid g(y)$.
Prove that $f(x) = x$.