I've been trying to figure out where to start with this problem and am quite lost. Any help would be appreciated.

Theorem:

Let Ck(x)= [x(x-1)(x-2)...(x-(k-1))] / k!

Then any polynomial p(x) with the property that p(n) is inZ, for all n inZcan be written as an integer linear combination

p(x) = (summation from 1 to k) MiCi(x)

with each Mi inZ, i = 1,...,k

Any help or place to start would be greatly appreciated. Thanks!