Question 86
Let $\mathbb{N}$ denote the set of positive integers. Determine all functions $f: \mathbb{N} \rightarrow \mathbb{N}$ such that $f(1) \leq f(2) \leq f(3) \leq \ldots$ and the numbers $f(n)+n+1$ and $f(f(n))-f(n)$ are both perfect squares for every positive integer $n$.