TW-TST 1996 Problem 6

Let $q_{0},q_{1},...$ be a sequence of integers such that

a) for any $m>n$ we have $m-n\mid q_{m}-q_{n}$ , and b) $|q_{n}|\leq n^{10}, \ \forall n\geq 0$ .

Prove there exists a polynomial $Q$ such that $q_{n}=Q(n), \ \forall n\geq 0$ .