Question 1
A function $f:\mathbb N\to\mathbb N$ on the positive integers satisfies $f^{f(n)}(n)=n^2/f(f(n))$ for every $n\ge1$, where the exponent denotes iteration. Determine all possible values of $f(1000)$.
Proposed by Evan Chen. Source: Evan Chen’s third-party solution notes.
Proposed by Evan Chen. Source: Evan Chen’s third-party solution notes.