Question 128
Given the set $P = \{1, 2, 3, 4, 5\}$, define $f(m, k) = \sum_{i=1}^{5} \lfloor m \sqrt{\frac{k+1}{i+1}} \rfloor$ for any $k \in P$ and positive integer $m$, where $\lfloor a \rfloor$ denotes the greatest integer less than or equal to $a$. Prove that for any positive integer $n$, there is $k \in P$ and positive integer $m$, such that $f(m, k) = n$.