Seems that there may be something missing. If x = 0, then since . But, what if ? Is the theorem (which I tried to find online with no luck) perhaps this?:
I've been trying to figure out where to start with this problem and am quite lost. Any help would be appreciated.
Let Ck(x)= [x(x-1)(x-2)...(x-(k-1))] / k!
Then any polynomial p(x) with the property that p(n) is in Z, for all n in Z
can be written as an integer linear combination
p(x) = (summation from 1 to k) MiCi(x)
with each Mi in Z, i = 1,...,k
Any help or place to start would be greatly appreciated. Thanks!