CGMO 2013 Problem 4

Find the number of polynomials $f(x)=ax^3+bx$ satisfying both following conditions: (i) $a,b\in\{1,2,\ldots,2013\}$ ; (ii) the difference between any two of $f(1),f(2),\ldots,f(2013)$ is not a multiple of $2013$ .