IT-CESENATICO 2008 Problem 3

Find all functions $f: Z \rightarrow R$ that verify the folowing two conditions: (i) for each pair of integers $(m,n)$ with $m<n$ one has $f(m)<f(n)$ ; (ii) for each pair of integers $(m,n)$ there exists an integer $k$ such that $f(m)-f(n)=f(k)$ .