Question 35
The function $f : \mathbb{N}^* \rightarrow \mathbb{N}$ satisfies that $f(2) = 0$, $f(3) \gt 0$, $f(6042) = 2014$ and if $(m, n) \in \mathbb{N}^* \times \mathbb{N}^*$ then $f(m+n) - f(n) - f(m) \in \{0, 1\}$. Find the value of $f(2014)$. Here, $\mathbb{N}^* = \{1, 2, 3, \dots\}$.