RO-NMO 2021 Problem 102

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: [list=1] [] $f$ is surjective; [] $c=0$ , $b<d$ and $0<a\le d$ . [/list]

Tiberiu Trif