Let $a,b,c,d\in\mathbb{Z}_{\ge 0}$, $d\ne 0$ and the function $f:\mathbb{Z}_{\ge 0}\to\mathbb Z_{\ge 0}$ defined by \[f(n)=\left\lfloor \frac{an+b}{cn+d}\right\rfloor\text{ for all } n\in\mathbb{Z}_{\ge 0}.\]Prove that the following are equivalent: $f$ is surjective; $c=0$, $b<d$ and $0<a\le d$. Tiberiu Trif